Seeing ice doesn't freeze the game - if the ice effect triggers while you're not moving, it does stop you from moving, though, so you do need to reset. When you're around ice you have to keep moving to make sure you keep some momentum once frozen.
We do agree it may have been nice to allow the player to do something when you're frozen but not moving :)
Tunan's diagnosis is correct. Unfortunately Godot runs inconsistent physics ticks, and if these start taking >0.1s our 'smoothing' effect loses out. The web version suffers from this most on weaker CPUs and browsers with slower WebAssembly runtimes. Try a native executable (or build from Godot source on our GitHub)!