Good question!

Given that GRRM based the Dornish Marches on the Scottish (and to a lesser extent, Welsh) Marches and their long and bloody history of reiving, I would say yes, although to a lesser extent than was the case before Dorne was incorporated into the realm.

In terms of who the fighting is being done by…reivers did not tend to be unaffiliated. Rather, you had a hierarchy of reiving “families” (who combined both actual family members and non-related members) from the very small who paid tribute in return for the protection of the larger families. So among the Daynes, the Blackmonts, the Mullendores, the Peakes, the Tarlys, Carons, Fowlers, Manwoodys, Yronwoods, Wyls, Dondarrions, Swanns, etc. I would imagine quite a few of their bannermen, and their bannermen’s bannermen and so on are reivers. 

In terms of the forms of conflict, you’d see a wide range from livestock raiding to reprisal raiding to protection rackets to blood vendettas to low-level warfare to full-scale warfare, carried out at various levels as bannermen call on their liege lords for protection and liege lords call their bannermen for military support.