There are many great areas in Minden/Gardnerville where you can find a nice home with some acreage for a horse. There is Jacks Valley, Foothill Road, Chambers Field, Ruhenstroh, and many more.
The regional medical center is located in Carson City, but is really no more than 20 minutes away from most anywhere in the Douglas County area. There are also smaller medical facilities in Minden and Gardnerville.
Call and let me know a little more about your dream home and I can send you information about homes that might meet your criteria.