Well I'd bite their arm off myself.
Let's assume you might think of having another baby soonish (big assumption I know), your parents are less likely to take 2 children for a week, your wife would have 9 months of pregnancy where most of that skiing would be out. Even if this is not the case, in a few years (which will go fast) she will be at school, and you will end up spending all your holiday covering childcare if you are both working. So you might not get another chance for a while.
A week is quite a long time to be away from your daughter and I would think twice given it's quite a lot of your holiday allowance, but assuming you don't get to do it every year, and you'll get at least one holiday away with her at another time in the year I don't see why not.
We went away snowboarding with our then 13 month old. We had a good time - we hired a nanny for a day and a half day, and got others in our group to babysit for a couple of hrs here or there, so we did get some boarding together. But it's not ideal - you aren't spending that much time as a family, which is what I enjoy - spending time in an expensive resort with not much to do for babies, with a non walking baby (at 13 months my son was tottering but had difficultly walking on the snow and didn't really like it, assuming your 10 month old won't be walking) while your husband is out boarding, is actually a bit crap. Sorry for being honest there, but I don't find every minute with my child delightful, sometimes it's a massive pain in the arse, much as I love him, and this wasn't the ideal environment from my point of view (to be honest wasn't helped by him being a bit under the weather and sleeping badly)
Just think - you could get up at 8am in the morning, and be on the slopes together by 9, or you could have LIE IN - your choice. You can get back from the slopes at 5, and have a beer instead of going "Oh flap flap flap what shall I feed her from the limited selection we have bought from the crap resort supermarket, will she go to sleep in the crap travelcot in the hallway?" and then you can go out together for a meal instead of having to cook in the self catering apartment as you can't go out without a babysitter!
Like I say, I'd bite their arm off. But I may be one of those selfish parents. Our snow holiday with him was good, but I'm not sure he got much out of being in a snowy environment (that's how my husband sold it to me, I wanted to skip the boarding completely that year), and from his point of view he would probably enjoyed pootling around with my parents for a week more.
Like joemarshall says, I love spending time with my son, but there are other things I love like biking and boarding that I can't do with him in tow. And I'm not going to feel guilty for wanting to do them, or wanting to have adult time without him now and then.
The only thing I would worry about would be whether she would be happy with your parents. Fortunately although my son doesn't see my parents that often he loves them and is quite happy with them. Like someone said 10 months can be a clingy age though.