I've done what you are talking about a number of times with biz trips to Vegas and Phoenix. A lot of the logistics though depend on your company's expense rules and level of strictness. What I would do is look at the roundtrip price from Vegas to where you are. Then, see if you can get two segements for the same or less money. Meaning the company flies you to vegas and then flies you home, from either Reno or SLC.
Then, you pay the ticket price for the in between segment out of your pocket. I've done both Reno and SLC this way. You can catch the first flight from Vegas to SLC and be on the slopes by 10:30am. If the dates are good, you could be skiing that first day free in Park City on the First Start free ticket deal.
Either way, it's worth it for two days for sure. When I did Reno, I did Squaw one day and alpine the next and I stayed at a cheap hotel on the edge of Reno and drove back and forth. If you're doing SLC, you can find cheap hotels in Sandy and drive (or take the bus) to BCC or LCC resorts.
You might need prior approval for the ticket or you might just ask forgiveness after but if the two segments are equal to or less than your roundtrip ticket, what's the big deal?