What size snake head did you use? Ideally, one the ID of the pipe with a cutter head. There should be no standing water in the pipe. There are only three reasons I can think of that would cause that: a collapsed pipe, or a belly, or a clog. The clog may not be total, and when some toilet paper or whatnot catches on what's there, it temporarily either slows things or clogs it momentarily. Unless the pipe isn't buried below the frost line, it should not get clogged from freezing. But, we've been having some quite cold weather, and the 'normal' frost line maybe inadequate. Usually, though, the local requirement takes this into account. A power auger in an inexperienced user's hands could lead to the loss of a finger or two, or worse. It is a powerful, dangerous piece of equipment.