Yes and the warm up is longer in winter :)
I slow down in the winter, I have less time and less daylight.
I only change the length of the session, standard in winter and shorter in summer because they get tired sooner and if you ask them things while being overheated and tired they won't give the 100% I strive for.
Same goes for warmup and cool down phases, which are both longer in winter to make sure the muscles are taken care of.
Because the shows are most of the time in winter, I do a more intense work during winter, and because of the weather and the shows less important in summer, I try to slow down and give them some rest during that period :)
No, I don't. Of course I'll adapt my lessons depending on the weather (if it's too hot, I'm not going to jump too much etc) but about the work itself, I don't change anything, maybe more canter on winter to let my horse romp :)