Is there a special way to avoid the layer of ice that forms inside a water bottle during winter activities?
You may have luck with a thermos flask, or similar insulated flask above a regular water bottle. If you're only going out for a day or so at a time the flask should keep the contents at a stable enough temperature so it doesn't freeze.
For longer trips, you may need a more elaborate system with heating to stop the ice.
You can use a Bottle Parka, which is basically a thin layer of foam that isolates the liquid from the outside temperature. Outdoor Research has a good one (Canadian website).
Also in winter, when I melt snow, I put the water in the bottle when it's hot near boiling, so it stay liquid for more time.
If you're gone a do overnight camping, you can dig a hole in the snow and put the bottle in there, cover with snow (assure you to retrieve it next morning). It's gone slow the process of icing. But next morning, heath this water a bit so it' won't freeze during the day.
I use a "Camelbak Stoaway" bladder - it has a bit of insulation and neoprene on the tube.
I fill it with warm water when possible and keep it next to my back. If not wearing it, I wrap my spare fleece around it on the 3 sides not facing my back.
The only other two things not mentioned here about bladders, I think, are that
I blow back the water after drinking and live with the fact that it might need cleaning more often.
I have slept with a bladder in my spare fleece in my sleeping bag on a cool night in North Sweden. For the tube ones I would attach a screw-cap instead of the tube first though!
My tip is to leave a bit of air in the bottle to make your movements cause the water to splosh. Moving water doesn't freeze as easily. Combine that with the other answer about keeping the bottles uppside down and/or in an insulator and your water should be readily drinkable.
Also: Pouring hot water in your containers might seem to be a good idea. However, some physicists claim that hot water freezes quicker. See Mpemba Effect