You've received a variety of answers here. I'll kind of throw in a couple more ideas.
On the question of why skin up *inside* an area, I can think of a couple of reasons. If you're not skiing with a partner, you're safer in-area than backcountry. Also, if you're just learning skinning and the gear, the question of snow safety is much less of an issue if you're in-area. You also may not yet have the transceiver/probe/training you need to go backcountry.
As far as skinning up a ski area, the policy seems to vary with the area. Some will allow it, others absolutely will not, some will kind of look the other way. If you do hike up in-area, be very intelligent about the route you choose. Stay away from congested areas and also make sure you're in plain sight from above at all times (don't hike below dropoffs and cat tracks). If the patrol "invites" you to leave, do so politely and quickly.
From a practical standpoint, once you've done the shakedown on the gear, you're going to decide that hiking up within a ski area's boundaries is nowhere near as much fun as going backcountry. Ask around at local shops for some backcountry awareness classes. Get the safety training and gear and find some partners. The skiing is great and you'll appreciate those turns a lot more.