Considering a more eastern route down. Winterpeg south?

http://trailsidervpark.com/ We stayed here. It's right off I-70.Nice,clean park with FHU.

As a general rule, the RV parks in the Kansas City area are open with full hookups all year round. And normally you will not have brutally cold weather for an extended period of time. That area of the country gets more ice/freezing rain than snow so you do need to keep an eye on the weather. But that is true where ever you travel during that part of the year.

When do you plan to leave? Last time I was in KC it was raining mid January but apparently that is not usual.

Yeah sure.