It might help if you told us what you drive, since different manufacturers have their own favorite ways of doing things. Also, there are sometimes different transmissions available in the same model, so one might have a 3-speed with (or without) an overdrive gear, and another might be a 4-speed with 4th having an overdriving ratio.
I drive a 1994 Dodge Caravan, and I’m still trying to figure out just how it’s supposed to work (“put it in drive and just go” works just fine 99% of the time). I have a column-mounted gear selector, and can choose from P-R-N-D-2-1, plus I have an overdrive lockout button (ODLB) located on the dash. If the ODLB is not activated, the transmission will start in first, then shift through second, then third, then (finally) to overdrive. In my vehicle, I suspect this is actualy an extra set of gears at the output shaft of the transmission (as described above). Some cars just have an extra gearset or so to give a fourth or even a fifth ratio, and gear them to drive the output shaft[s] faster than the input from the engine.
If the selector is in “2”, it starts in second, but will shift to third (possibly the overdrive – I don’t lock it out most times). When I select “1”, it starts in first and shifts to second (once again, maybe the overdrive). My van isn’t quite like new and I’m not certain if it’s really supposed to work this way, and since the owner’s manual is kind of vague about how it operates, I can’t be sure. From perusing the manual (it’s different in many cars) I do find that they recommend I leave the ODLB alone unless I’m driving in hilly/mountainous terrain or traffic where the transmission is frequently shifting in and out of top gear. Locking out the overdrive will keep it from shifting into overdrive.
As far as driving on slippery surfaces is concerned, what you are ideally trying to do by “downshifting” isn’t to put more torque to the road, but less. Starting in second, rather than first, puts less power to the slippery surface, reducing the chance that one tire or the other will slip. Unless you have a limited slip differential, a slipping tire means all the power from your engine is wasted turning he wheel that’s slipping – no useful power goes to the tire that still has traction. Reducing the power going to the wheels by starting in a higher gear reduces the chance of one wheel slipping. This allows you to start moving sooner with less drama than in a lower gear. When starting from a stop on a slippery road surface, you don’t want to start in first, but second. Leaving the car in “D”, you’ll start in first gear (as will shifting it to first).
Some of you manual-only people might protest that starting out in a taller gear than normal will cause the engine to “lug”. Don’t worry about it. A car with an automatic transmission can’t lug its engine. Otherwise, you’d have to shift into neutral whenever you came to a stop to keep the engine from dying (I’ve owned cars that worked like that, but it wasn’t the transmission’s fault).
~~Baloo