I'm not sure why, but almost every time I pull out of the garage, there's a small puddle of coolant right under my right rear water pump hose (the funny one that goes to the coolant tube that runs under the length of the car). The hose is brand new and the clamps are on there good and tight, but for some reason this coolant appears every morning. The hose has been completely dry every time I checked. Could this be caused by the cold temps? It has been getting down to -10 every night for about a week.

No, for sure you have a leak! If the hose is new, you should give the clamps a turn or two. Hopefully that will clear it up.

Was the water pump replaced when the new hoses were put on? Is the coolant coming out the weep hole and traveling down the housing and hose to drip off at the lowest point?

Yes, the waterpump is new. In fact, the entire engine only has 2k miles on it. Funny thing is, there was no puddle this morning. It was quite a bit warmer last night though.