Disc brake freezes up
Are you using cable disc brakes? If so, is the rear caliper mounts to  the chain stay or the seat stay?  If it is the chain stay, the brake cable will likely dip down then run along the chain stay (see picture).  If the brake caliper doesn't not have a cable boot (most systems except Avid BB7) water can enter and get trapped in the cable housing.  If there is water in the cable housing, when it is freezing out your rear brake will quite literally freeze up.



This won't happen on the front brake because the cable housing is vertical so water will continually drain out.  This is also true for rear cable disc brakes mounted on the chain stay.

Solutions

If you bring your bike inside to thaw, then you can hang the bike rear wheel down to let the water drain from rear brake the housing.  If this doesn't fix the problem (water cohesion may retain some water in the system) you can also try evacuating the water with oil (then the drain the oil out of the housing to reduce the amount of dirt that will be attracted).  Finally, failing all else, you can replace the cable and housing (but riding in the rain will send you right back to where you were when it freezes again).

This is an unfortunate side effect of mounting a brake caliper on the lower (chain) stay and not fully sealing the cable housing. As an aside, mounting on the chain stay makes it easier to mount rear pannier racks, which is a much more difficult task when mounting the caliper on the seat stay.