I doubt that you will be to happy trying to grow Mugo pine.
It is an alpine species from the high mountains of southern Europe and does not tolerate our climate. They survived only a few years for me and that was in the years when we actually had Zone 7 winter temperatures.
You might try one of the Chamaecyparis cultivars, from one of these species: C. obtusa, C. pisifera or C. thyoides. I grow several cultivars of the first 2 and they perform well for me. Here's a link to list of the more popular cultivars of C. obtusa and some photos of C. pisifera * C. thyoides from down under.
C. obtusa
Rb

Here is a link that might be useful: Chamaecyparis pisifera & thyoides

I have three of them and, so far, they are doing OK; although I have had them only one year. They were an experiment though, so if they don't make it, oh well. Live and learn. I had three Chamaecyparis (miniature) also. One of them is on the other side of a big rock from one of the mugo pines. Both of those shrubs are doing better than the other four. Shade from the rock? Shade from the nearby crape myrtle? Not sure. One of my Chamaecyparis kicked it pretty quickly after planting. We are not sure why, except maybe Southern Blight or root rot. The other two (that get a little shade in the afternoons) are doing better. Weird, huh? Would've thought the full sun would've been better for them. I have found that a LOT of things I thought required full sun actually do a little better in our climate with a little shade in the afternoon. Especially plants that are considered good "rock garden" examples (sedums, those mentioned above, etc).

Mugos like soil with good drainage and clay won't cut it for long. I use them rarely in landscapes and only when I can plant them slightly raised or in excellent drainage. Razor is right on with the Chamaecyparis suggestion. They do great here and look really good as they get bigger. Plus they come in several interesting varieties. My favorite is C. pisifera 'Gold Thread Cypress'.