Generally, I doubt a little bit of snow/ice/frost would penetrate deep enought to have much effect. Not enough volume of water there. But add that to a wet year, a fair bit of rain, etc., and you could have some highly interesting action. It's all cumulative, and you won't have any knowledge of most of the "accumulation" when you show up in camp.

You could, of course, warm the rocks slowly. Build a rough cairn around a small-stick fire and keep it going. You're unlikely to create enough heat to make steam, and the rocks will still heat up slowly. Over time, you will get what you want.

On the other hand, if in doubt, and wood is plentiful, fire 'em all hot and stand well back. Once the fire is down to ash and coals, you're unlikely to have any big booms in the dead of night. So you can sleep tight. (Don't look in the mirror next day, though; you'll be wearing enough soot and ash to make small children go screaming to mommy. :-)