I have never been that hungry that I would chase my food through freezing lake water. If the wolf doesn't get the deer think of the energy wasted in the chase then drying off afterwards.
I feel like if the deer gets to land before the wolf, the deer is going to be fine.
Deer are very capable in the water. I knew two guys once who were duck hunting and saw a deer swimming across the lake. They jumped in their boat and went out to the deer with the intention of drowning it (illegal) and taking it home to eat. Both of the guys ended up in the water and vowed never to take on a struggle like that again.
"Fuck off! Seriously?" That's what I would be saying if I were the deer and spoke English.