We are relocating from OR to AZ and needing layovers for 4 horses in Twin Falls ID and Las Vegas NV. 

The fairgrounds in Filer will probably be your best bet in Twin Falls. They have good stalls, RV hookups and nice bathrooms with showers. I imagine they're open through the winter but you might want to call and check first. 

Contact Horseman's Park in Vegas.  You should be able to Google a number.  It's right behind Sam's Town off of the 95 and i believe you can overnight in your trailer if you have an lq.  If not it's a 2 minute drive to Sam's Town 

When we travel fairgrounds are usually always open or saddle clubs and some cabella have a set up for stalls with water.