Modern passenger do have some protection against ice. Bleed air from the engines -as already mentioned- is used to de- ice the more critical areas, for example the leading edge slats.
Here are some of the anti-icing features of a Boeing 737
It’s worth mentioning that the latest passenger aircraft do have features to warn the aircrew is icing condition exist ( even if they didn’t already know). If you read my link there are some pictures of how the aircrew can see ice forming on the windscreen wipers for example
As you yourself say aircrafts are already equipped with de-icing systems that are powered by bleed air. And as this shows, de-icing systems that use bleed air to de-ice wings are also available. Realizing the severity of the issue, knowing that it is something that has been an established reason for many crashes, isn’t it only prudent to install these systems on planes no matter what the cost. I mean, after all, how much would the extra tubing/valves etc cost that could not be compensated by reducing the payload by a few passengers/luggage, other unnecessary gadgets.
So what exactly is it, that airlines still continue to risk passenger and aircraft safety, and also continues to spend millions in deicing aircraft before every flight using the liquid spray?
Wow, apparently I freaked a few people out with the NTSB’s report.
As to the removing ice issue: We are talking about two separate processes here. The first is to remove all ice BEFORE the airplane takes off. This must be done on the ground with additional equipment (like a deicing rig). There is no way to practically heat ALL of an airplane’s surfaces in order to remove ice/frost before takeoff.
The anti-ice systems installed on airplanes (and yes, the Challenger that crashed had them) are to prevent new ice formation on the wing leading edge and other areas (hence the term “anti-ice”, not “de-ice”). There are some airplanes that use de-ice equipment in flight, but most jets use anti-ice equipment.
So, what happens when it’s sleeting outside? You get your airplane DE-iced by a de-icing truck. You then get a “holdover time” which is the amount of time that you can wait before either getting airborne or having to be de-iced again. This time varies with the conditions and the type of fluid used to de-ice the airplane.
Once you are airborne ice formation on the TOP of the wing is not a problem: any precipitation will impact the leading edge of the wing first (you are moving fairly fast, after all). Thus inflight only the leading edges of surfaces need to be anti-iced, and they are.
If you follow the proper procedures you can operate safely in extremely poor weather.
What MIGHT have happened (it’s all speculation until the NTSB releases the final report) is that the Challenger crew decided that they did not need to be DE-iced before takeoff. A small coating of frost on a wing will change its aerodynamic properties, resulting in less lift and more drag. Given a long enough runway and enough power you could probably get airborne, but put that same aircraft on a short runway and you could be in trouble.
To summarize: outside equipment is used to remove ice from an airplane before takeoff. Once airborne, onboard systems prevent ice formation on the surfaces where it would accumulate.
And just to emphasize the point: if proper procedures are followed, your flight in winter weather will just as safe as one on a clear summer day.
Please don’t WALK everywhere: you’ll get wet and catch a cold!
The ice protection system that you have cited is no different than any modern passenger aircraft has. Ice protection is concentrated on what is perceived to the critical areas. To have protection for the entire wing would need more power from the aircraft’s bleed air system than is available ( I assume you’d like the aircraft to have enough power to propel itself through the air?)
It would not be a matter of more “tubing valves etc.” either. A large part of the construction of the wing contains integral fuel tanks which would present many technical difficulties with your tubes.
Nor am I convinced that statistically there are “many crashes” caused by icing up of wings. Of course 1 is too many but nothing is 100% safe.
I’d also like to know what these uneccessary gadgets that aircraft carry about that you can omit to accomodate all these extra tubes and valves.
Whether you like it or not aircraft have to be cost effective.
Yet another example of why pilots should leave explaining things to the passengers to the flight attendants. 
Well, not YOUR airplane, no - smaller airplanes can be placed inside a heated building. That’s MY personal preference - if I’m flying in winter I like to have the plane inside a heated hangar overnight so it’s frost-free and dry when I take it out in the morning. Mind you, the hangars aren’t kept tropical - about 40 F degrees is all you need. That’s what? 5-6 C? (for you metric types)
Doing this with 747’s presents certain practical difficulties, however.
And this should be emphasized to all the nervous flyers out there - proper procedures will result in safe flights. You have almost certainly flown in conditions conductive to airframe icing, yet you lived to tell about it.
Correct me if I’m wrong, Pilot141, but 6,000 feet isn’t particuarly long for the type of jet that crashed, is it? Adequate for most conditions, but if you need to abort a take-off it doesn’t give you much braking distance, does it?
In addition to the frost, other things the NTSB will be looking at is whether or not the pilot made the decision to abort the take-off in a timely matter, and whether or not the runway was of adequate length for the conditions at the time. Also whether or not the runway was cleared of snow/slush/ice/water - any one of which could seriously reduce brake effectiveness and steering. Ice may be a contributing factor, but likely it’s not the whole story here.
I’ve had to abort take-offs due to loss of power and inadequate lift - no accident occured. On both occassions I had dry pavement, working brakes, a steerable airplane, and adequate distance to bring everything to a halt. Presumably, the pilot in this accident was attempting to achieve the same success but did not. The question is *why? * It’s not just the frost that lead to this outcome.
Would also possibly impact the employment of some of your fellow Dopers, right Pilot141? 
You are correct. Rwy 6 at TEB is 6013 ft. A lightly loaded CL-601 might need about 4500 or 5000 feet for takeoff (I’ve never flown the Challenger, so I’m just guesstimating based on experience). Note that this is really the runway required for an abort - the airplane will probably be airborne in 3000 feet. Also, the distance is predicated upon beginning the abort AT V[sub]1[/sub] (decision speed). If you delay the decision to abort all of your takeoff data is worthless.
If those pilots got to V[sub]1[/sub], then V[sub]R[/sub] but could not get airborne due to frost on the wings, they would have begun the abort WELL beyond decision speed and with very little runway remaining. The result: going off the end of the runway at high speed.
As for everyone walking, yep, a small attempt at some career protection! 
FWIW, this might not have been icing-related at all. The pilot told the company’s lawyer (you knew there’d be lawyers involved immediately, right? This is America, after all) that he aborted because “something broke”. The recorder isn’t much help, either, unfortunately.
Q: How many air crash investigators does it take to change a light bulb?
A: It’s too early to speculate on that at this time.
Well, the OP asked how frost could cause a plane crash in a sort of general way.
But yeah, that report that there may have been no ice is an illustration of why the NSTB keeps banging away at the “too early to speculate” line.
“Something broke” is an entirely possible cause of the New Jersey crash - one of my take-off aborts occured when the engine quit during the take-off, which certainly qualified as “broke” in my view.