Any food with heavy use of food coloring, frosting included, has the potential to stain if applied to exceptionally dry areas (e.g. certain areas of feet) or in nooks/crannies (e.g. under fingernails, skin folds on hands/feet). Also depends on how long you're sitting or wallowing in it. 10 minutes isn't going to stain as deeply as several hours.
After a couple of showers, it tends to wash out or, over time, it bleeds out with showers, etc. If you're caught with blue hands and feet, as I was for a photo shoot a month ago, I just state I was part of an art project.
We havent had any issues with staining from icing. Even on white clothes it washes out. Now granted we wash up right away and dont let it dry. I think that may be where you will run into more of an issue. It would be fun hearing you explain why your skin is tinted though.
Frosting has been my go-to substance over the past couple of years. I've done white, chocolate and dyed colors like pink, orange, blue and purple. I agree with Gungedawg: Time matters. If I'm wallowing/playing in it for more than about 30 minutes, the purple and blue frostings can sometimes leave a tiny bit of color behind on my skin. Like a hue. To me, it's barely noticeable. But I can understand that it might bother others, or be more noticeable based on your skin color, what you're wearing, etc. It takes either extra scrubbing in the shower OR just waiting a day or two for it to fully go away. Again, it's only been an issue for me with blue and purple. I've never had that issue with white, chocolate, pink or orange frosting.
We've used the large tubs of frosting you can purchase at select Sam's Clubs (or orderr online) and haven't had a staining problem. However, we've stuck with lighter shade - white, yellow, etc. - and avoided the darker/heavier colors. As others have noted, wash the frosting off as soon as possible and you shouldn't have a problem.
I'm on the other side of the boat on this - I love to find things that stain my skin. So if you find a type or brand that stains, I'd love to play with it!