Personally I'd only consider keeping the ice if it were not a very common path. If tanks and infantry had no choice but to cross the river (no bridges or land bridges), I would definitely swap it out for water.
If however the ice is a shortcut that players can choose whether or not to take, ice can add that extra risk factor.
Something that I was planning a while back is to have a partially frozen river that allowed access to some areas in the early game, but as time went on, it allowed more opportunities as it froze entirely.