I found my stylus which was in a pencil caddy and the sliding/dragging action works fine.

I don't have mittens, but if I put my hand with the four fingers opposing the thumb, then I am able to hold the stylus in a winter glove. Feels a bit awkward, but definitely able to use the phone. You can't do multi-finger gestures though and that could be useful to zoom in/out on a map.