I spent about 3 hours in one single afternoon at the Round-Up last year (mostly taking photos), then went back a couple of days later and had a long chat with a CM who worked there (trying to recall her name - it might have been Velora). You definitely cannot pet the reindeer now. I'm not sure what they did prior to last year, but at least as of last year, for sure, there was no petting.
First of all, as the CM told me, reindeer are not particularly friendly. Then there is the issue of the overzealous, excited children who agitate the reindeer...
Not only can you not go into the area to pet the reindeer, but the decorators and CM's actually put up extra 'stuff' beyond what they would have normally put up (just as 3Minnies1Mickey said above) all around the boundaries and perimeters of the petting zoo, specifically to prevent little tiny hands from worming their way through the slats in the fences or any random openings they could find.
Still, these festively designed barricades (comprised of assorted things like barrels, crates, haystacks, big planters, wagons, reindeer knick-knacks, etc.) will not stop the super-determined children, and the CM's found that kids were climbing up on some of the crates, etc. to try to get their hands and arms over the barriers anyway, and the CM's had to keep asking them to step down or ask the parents to take them down.
So you basically just get to observe the reindeer walking around, sleeping (they breathe very rapidly when they rest), eating, drinking, etc.