Skiing:
Arizona Snowbowl is outside Flagstaff on the way to the Grand Canyon
http://www.arizonasnowbowl.com/
Brian Head is in Utah, not too far from Bryce
http://www.brianhead.com/winter

Lots of spa options for Las Vegas and Sedona.

2 nights in Vegas, 2 at whichever ski area you choose, 2 in Sedona, one at Grand Canyon, one at Bryce and 2 in Springdale to visit Zion.

You would want to stay in the park at the Grand Canyon for an overnight visit. If you want to limit the number of hotels, perhaps you could base yourself near Brian Head and visit Bryce Canyon as a day trip instead of staying at Bryce overnight. That would get it down to 5 hotels in 10 days.

You might need to bring something like Yak Trax. The parking lot, sidewalks and steps were all covered in ice when I was there in March.

You probably won't be able to get into the north rim. It's a long way around from the south rim to Bryce but worth it if you have time.

Thanks for comments. Lots to consider
Er. Any specific recc on where to stay in canyon and at various locations

In GC, get a reservation at any of the places in the park. elTovar is the nicest, historic hotel on the rim; also on the rim, Bright Angel has cabins and a lodge, some with shared toilets Thunderbird and Kachina are typical motel type places, clean but basic except for location. Maswick and Yavapai are also motel type places but a short walk back from the rim.

The reason to stay in the park is so you can be there for sunrise/sunset and not have to drive in the dark on roads that often have deer and elk on them. You should have no trouble finding something in park and can make a cancelable reservation and change it if something you like better comes up later.

Fooey - lost a post getting this webpage - for the Mt. Charleston ski area - just outside of Vegas. http://www.mtcharlestonresort.com/

Anywho - I would recommend you head over to the Grand Canyon after landing in Vegas (5 hour drive) and then after a couple days on the rim (either at El Tovar or Bright Angel) - go to Zion/Bryce, and then you could ski at nearby Brianhead (the largest of the 3 mentioned) - or head back to Vegas to kick back and stay in one place for 3 or 4 days and drive up to Mt. Charleston - or spend a day or so up at their lodge.

We love Wynn's resort - but also like Bellagio - and their great pool/fountains/arboreteum is more central strip.

And for Zion/Bryce Canyon accommodations - unless you base at Brianhead ski area for a few days - then the town just outside Zion - Springdale? - probably has the best choices and you could even use that as a base for all three areas.

Here is a little more info for Springdale - and also check other posts in here under Utah, Arizona and Nevada for more information on these places.

http://www.tripadvisor.com/SmartDeals-g61001-Springdale_Utah-Hotel-Deals.html