gymrat, my only concern for you and winter brewing, is that it's just not cold enough in Kansas
Winter in Michigan is my main brewing season, and although it can be a hassle, it has multiple benefits:
a) Super easy to cool off ten gallons of wort to lager pitching temps with even a small chiller
b) Use a cheap pond pump to circulate snow-water through the chiller
c) No fruit flies, and the general airborne presence of microbes is small
d) Which makes it safer to do things like rack to the fermenter outside (covered big shed) and aerate out there, further dropping wort temp
d) My cellar gets down to 50 and stays there for months, so between the fridge and the cellar I have lots of options
e) It's winter, what else am I going to do between shoveling the sidewalk; take up ice fishing again?
I don't really need the outdoor tap, but I usually use it. As others said, keep the hose inside overnight. When you are done with the spigot, close it off and let it drain. Not had a problem in four years of this strategy.
As other have said, if you have a good cooler, your mash temps will hold surprisingly well. My best cooler wrapped in an old Coleman sleeping bag or two hardly drops more than a couple degrees in an hour even at 10 F outside.
On the other hand.. it does take more propane, and I sure could use all that heat inside the house - so I often do what others have mentioned, downsize and go to the kitchen stove depending on mood.
Watch out for ice patches!