Will be moving from Indianapolis to Las Vegas in December. Will I be able to get through I-70 in Colorado or does the Interstate close in the winter due to snow?

Sometimes, but not usually for more than a day.

You shouldn't have any problem with it closing; that doesn't happen too often, but it depends on weather, of course. But you should take special care when driving over those passes in winter. If you aren't prepared, it can become a terrifying experience.

Make sure you have good snow tires (or chains may be required) on your car, and that you have the proper items in the car in case of emergency (like driving off the road and careening down a mountainside into a snow bank, where no one can find you for days. Don't laugh, it happens).

Take I-44/40. Much better route in the winter.

I think it would be unusual in December for I70 to be closed. Just watch the weather news. The bad pass is through the Eisenhower Tunnel for ice. If chains are required, just stop for the night.
Might not be a bad idea to drop south as suggested--you'll need to do it anyway.

I-70 is rarely closed at Eisenhower, esp. in December (unless some idiot young male skiers have gotten into an accident); the worst closures are east of Denver, toward the plains. (Go south anyway, and avoid the possibly of horrendous backups of people returning from skiing, esp. on weekends.)