Guessing you don't have a load of weight in the boot/trunk - ie, giving the drive wheels less traction?
Sounds like bad tyres. That's all it can be - if the wheels are slipping. Hydroplaning is pretty cool but pretty dangerous, I'd change the tires (damnit.. am I British or Canadian, argh) ASAP. Because if they are slipping when moving, it's sure they'll slip if you try to stop in a hurry...
Do the depth test I guess. See if one side is wearing more - in which case, only part of the tire might be gripping properly. And/or when you get the new tires on, get the shop to do a tracking/alignment check. Don't bother if the tires are wearing evenly though.