Heated shields work great for trail riding, as well as for wives and kids. However, they are quite terrible for most mountain riding. You're typically on and off the sled too much to stay plugged in and an unexpected roll over could be an issue.
The main reason, though, is to separate your eyes from your breath. In mountain riding, you work and breath so damn hard that you'd be fighting fog up constantly. Then, if your shield gets all messed up with snow and ice, which will happen, you can't easily swap it out, like you can with another set of goggles.
Get some quick straps and you'll never think of using a shield again.