It's almost completely up to the command unit and the mission. I would be shocked if more than 1% of MDs or PAs in the Army have every been on a real dismounted infantry/spec ops foot patrol. A lot of it is about the luck of being in the right place at the right time. We often took a PA or a MD on certain patrols with us, those patrols being ones where we thought a high chance of close combat or dismounted IEDs. We had one doc who loved to go, he was a former enlisted infantry guy. We had one guy who hated to go, he was highly skilled specialist who never failed to mention that he had no desire to deploy, let alone leave the wire. That said, we operated for a year in the worst part of Afghanistan in 09-10. The story of the second guy is the what makes me personally question military med: as soon as he left residency (and I believe a fellowship), he was stationed in the mid west, and then assigned to our unit on the other side of the country for 4 months prior to deployment, but was NOT allowed to bring his family b/c it was less than 6 months actually assigned there. Then he was with us for a 13 month deployment. All told, he spent 17 months away from his family and doing virtually nothing of what he had worked so hard to master.
As far as SF, I know its possible to be an MD out on mission with them, but I can't imagine why they would. My experience with 18Ds (SF medics) has been phenomenal. Ranger batt would be a great gig, but you must graduate ranger school. Of all options, I would imagine you would be most likely to leave the wire if you were a tabbed PA in Ranger Batt.