I don't know what state you live in so I won't comment about LL liability.
But It doesn't sound that you have a problem that you can't fix simply by yourself.
Ice on the inside of the window begins with excess humidity.
Look into that. It then condenses out on the cold window pane, and even may freeze if the pane (not the room) is cold enough. This is not unusual in cold climates without anything being wrong (I didnt always live in California). See if you can't reduce the humidity.
If there is cold air blowing, its probably not through the window, but around the frame or the glazing on the window to the pane. Run your hand around the window frame to locate where it is blowing, buy a cheap caulking gun and some painter's caulk and squirt the caulk where you feel air blowing. Spread the caulk into and around the hole with your wetted finger. Another approach or adjunct is to use plumbers putty. Roll a piece around in your hands to soften it up and push it into any holes that you find. Neither of these fixes should cost you more than $5.
In California, LL is required to fix a window which is not watertight (seriously not watertight, not just a little air blowing through, or even drops or a small stream of rainwater, but something that is a genuine health-threatening problem). Most cold-weather states approach your problem by mandating a minimum temperature level and not caring about stuff like air leaks. If the heating system can't keep the room temperature above the minimum, then LL has to do something for you.
