Yes. It is way more fun and interesting to hunt them in the snow. Get some snowshoes and wear the right clothing and you'll have no trouble keeping warm, even at a slow pace.
As far as tracking the flushed ones goes, all you need to know is that they usually only go between 15 and 30 yards and then they jot left or right and sit tight behind something. In my experience, in my area, they go left 8 times out of 10. I have no idea why, but I've learned to count on them going left. When they hear that you are still on their trail, they usually hop cautiously in that same direction in an effort to eventually circle back to where they came from. This is something else I have learned to count on.
Knowing all this makes it easier to "cut them off at the pass", so to speak. I usually proceed in the general direction they went for a few paces, then start veering to the left as I continue. When I play it right, they have started to circle back around to my left and we end up face to face. Even when it doesn't work out perfectly, this strategy allows me to get different views beside/behind objects. Walking straight forward, one's view of the landscape doesn't change much with respect to the hares' possible hiding spots, but walking on a diagonal allows more perspective change - a more variable view in/around trees, logs, etc. Often this sideways movement is all that is needed to reveal them. I use this technique even when I am standing still; moving my torso from side-to-side, up and down, to change the position of my head and hence my perspective. So many times this has been just enough for me to spot an ear, an eye, or a shape/shadow. If I don't "head them off at the pass" or notice them hiding somewhere as I walk diagonally left, then I either see them bolt again or they are sitting right beside me, hiding "in plain sight".
The thing to keep in mind during this whole game is "always be looking for other hares". Just because you saw one hop behind that tree 20 yards away doesn't mean that is the only hare in the area. Also, if you shoot one 30 yards away keep hunting while you are on your way to pick him up. I can't count how many times I have shot a second one on the way to collect a dead one.
Still, remember that there are good days, average days and bad days. If you get skunked 3 or 4 times in an area, go back 3 or 4 more times.