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.
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.
LOL... I'm sure he didn't succeed. That would be a really hard kill in the water -- wolf would have a bigger chance of drowning than killing the deer.
Heck, that would be a tough kill for a lone wolf on land. Wolves aren't like big cats that can more easily take down bigger games by themselves due to their flexibility and agility that allows them to go for the throat.