flushing a heater core

Recently, as it got cold hear, I learned my car does not have heat. I checked the heater core, which wasn't leaking, and checked to make sure that the vents opened up properly, which they did. I figure there must be something stopping up the heater core causing it to not circulate antifreeze. I know I am going to have to flush it; What is the best way to go about doing this? Normally I wouldn't be that concerned, but it is 25 degrees where I'm at with snow on the ground, so hooking up a hose and flushing it ouside right now is not a good option.

Thanks