There wont be an oil light, and that red leak could be coolant as well, they're the same colour. The oil from the transmission is thicker in appearance though.
If it feels like you are driving on ice, this means the transmission is slipping. You wont really do any damage to it unless its slipping. If the leak is a couple drops on the drive way then I think it's safe to use, but if it's leaving a puddle. You shouldnt drive it.
To check the oil level in your transmission is pretty complicated if you dont know what you're doing, and the only way to check it is to drive it anyways.
Best thing might be to take it to your mechanic and have him check it, and add more fluid if necessary, if you really want to drive it this weekend.