It's not really a good idea to over handle any reptile. And I certainly wouldn't let one explore the house. They can find any dark crevice and hide very effectively. Now in an enclosed lizard proof room while you're watching, a larger lizard could explore a little just fine. Don't know a lot about Mtn. Horned Lizards except I haven't seen them as readily available as some others. Whatever you do don't buy anything wild caught for your first reptile.
Oh and in response to Breawna, no offense intended whatsoever but you may want to reconsider the source of some of your info. I have kept reptiles including beardies for years and enlist the advice of many others who have done it much longer and I can say with strong confidence that there is no reptile on earth that benefits from daily two hour handling. Even reptiles that tolerate handling only tolerate it and would in my opinion become quite stressed out at this level of human attention. Please anyone with a reptile or considering getting a reptile, get them because they're gorgeous and unique and interesting to watch in their natural behavior, do not get them because you want something you can play with. Hundreds of animals die every year because of this very mistake. Sure there are some who stress out less and tolerate handling more than others, but it's all relative, none of them love a large amount of it. This is exactly why I have gorgeous geckos, chameleons, snakes, and uromastyxes for watching, and rats for cuddling.