Well for the hell of it I just tried Skyrim on the Intel HD 3000 and more or less found it to be playable as long as expectations are kept low. I did a pretty decent amount of play through getting up to level 10. Since the Intel HD 4000 is in general 30% more powerful than the HD 3000 playing Skyrim is doable as long as expectations are still kept a bit low.
Running Skyrim on an Intel HD 3000 takes some work though; meaning you need to make some modification even after setting the game to the lowest resolution of 1280 x 720 and everything set to low settings, but textures are kept at high since below that it simply looks terrible with everything set to low as well.
Without getting into too many specifics the SkyrimPref.ini file needs to be edited to turn of shadows and lower water quality settings. A google search will help you out with that. You also should google for reduced sized texture mods to help improve performance as well.
Anywaste, as stated I found the game to be playable enough with decent frame rates ranging from about 22 - 45 FPS in most cases, but rainfall & snowfall can drop it below 20s so you also need to google for a mod that lowers the performace impact as well. This is plain vanilla Skyrim and none of the DLCs. The Intel HD 4000 should give you roughly high 20s to low 50s FPS. Skyrim is one of the more intensive / demanding PC games currently out.