The drone keeps it's altitude with a barometer, you should have no issues whatsoever maintaining a constant altitude while you fly over the frozen lake assuming the drone is operating correctly. I wouldn't suggest flying extremely close to the ground to leave some margin for error, but that is up to you. The downward sensors can be less effective when flying over a monotone/reflective surface such as snow, but those won't be what is keeping your drone's altitude.
Keep in mind if you are flying fast & low, you will likely need a faster shutter speed than 1/60 to prevent everything from being blurry.