I know that it defies Newton’s Laws but my students are convinced that when they have exactly the same skis as someone else, the heavier person moves faster.
I wonder if there is a reduction of friction similar to skates on ice.
Can anyone offer an explanation?
Yes, heavier skiiers tend to go faster just like heavier people go faster on waterslides all other things being equal.
This site has a good breakdown of the physics. at 15.2
The basic reason is that added mass helps overcome surface friction.
(Made up numbers) If you have a 5 % increase in frontal area and drag but a 20% increase in mass, the heavier skier will go faster.
Think of dropping a ping pong ball and a lead weight of the same size and shape off a tall building.
There can be limits. If the ski was too tiny, then it sinks into the snow and the ski is then angled up and digs a deeper track.
No, surface friction is (at least roughly) proportional to mass. The difference comes mostly from air resistance.
You lost me here. If the frictional force is proportional to mass and air resistance is based on size, shouldn’t the smaller person go faster?
Big fat-ass here (225 lbs). I do, but its because I’m a much better skier. 
You know more about physics than I do but I respectfully disagree. It isn’t about air resistance in this case and the cite I gave above shows why. Put a small child and a grown man on a waterslide. The man will go down much faster even in the prone position where air resistance isn’t a big issue (I do it with my daughters every summer for a race to the bottom on parallel slides and I always win; there is no skill involved). The slide has surface resistance that has to be overcome and raw mass is the biggest factor in overcoming that. It is the same thing with skiing on groomed ski slopes. Snow has inherent surface resistance that you have to overcome before you can go really fast. The drag on a small person versus the heavier one is the biggest factor in that equation unless you are talking about unusual circumstances.
Overcoming air resistance is a factor but only a moderate one especially at the speeds that most small skiers achieve. Surface resistance is much more important in this case.
Skiing physics
here http://sportsnscience.utah.edu/skiing-its-all-about-friction/
and
here Physics Of Skiing
and
here http://biomekanikk.nih.no/xchandbook/ski4.html
Note this last analysis is for cross country skiing
I was going to say that the impact of skier weight is negligible compared to other factors, such as the skill of the skier or the quality and condition of the skis, but I see those have already been discounted.
Your cite says the same thing I did.
Your first link shows that drag is proportional to the normal which is proportional to the force of gravity. Therefore, a heavier person will have more drag.
Can you discuss this in terms of static or kinetic friction or am I on the wrong track?
No, because force due to gravity is also proportional to mass. The effect of the net force is divided by mass in order to become acceleration, but that’s after you subtract the forces from ski friction and air resistance.
Does that help?
Newton’s Laws are good in a vacuum (well up until near the speed of light). Note what runner_pat said.
I’m a ‘Clydesdale’ cyclist meaning that I weigh quite a bit more than those skinny Tour de France professionals. Downhill I could probably beat most of them. I often have to get on the brakes to keep from overtaking other lighter riders on long descents.
I go faster and I’m not a better skier.
Force pulling you downhill is proportional to slope and mass. The heavier the skier, the bigger the force.
Resistance, it seems, is proportional to surface area more than pressure on skis.
Most skis have about the same surface area; so, about the same resistance.
the extra weight, the extra downhill force, the faster you go.
(On packed snow, it also seems there’s some sort of “pressure makes slippery” effect. Every skier is familiar with the idea - put too much weight on a ski and it starts to slide on hardpack…)
No, you don’t. 
And no, you’re not. 
Look me up the next time you’re in Tahoe and well test this proclamation.
Loser buys the beer.
Another very significant factor is muscle strength, which is stronger in heavier skiers (assuming similar physical conditioning and technique).
In alpine ski racing disciplines, the skiers must move on and off of their edges to make their turns without going off course. The stronger the skier, the more speed the skier can hold throughout the turn. That’s why the best alpine ski racers tend to have very large upper leg muscles.
Have a look at times for women and men who are running the same course. Usually the top grouping of men will have faster times than the top grouping of women. It isn’t technique that causes this difference, it is muscle power, which is proportional to muscle mass, which is proportional to a skier’s weight.
BTW, we had a good discussion on this issue a few years ago on the SDMB.
True, however, a heavier person will have an advantage on a rough course by being better able to ride out/cut through the ruts and irregularities rather than be bounced about by them.
That gets into the surface friction being only a rough approximation. Honestly, I wouldn’t expect it to be a particularly good approximation, on a surface like snow; it’s just not clear to me what to replace it with (though I’m sure people have studied the problem and come up with better approximations empirically).