During the era when the Red Kings of Dreadfort fought on equal terms against the Kings of Winter for hegemony over the North, which Houses do you think are likely to have been their allies/vassals against the Starks? Conversely which Houses do you think backed the Starks?

You mean before the rebellion that involved the Greystarks?

We also know that Bolton power once extended up to the Last River, where the Umbers now rule, and down to the Sheepshead Hills, where the Manderlys now rule – given the scale of territory we’re talking about, they must have sub-infeuded their fiefdoms to various vassal Houses.

Naming specific houses is hard, because I think the Starks eliminated a lot of them in the process of subduing the Boltons – hence the creation of the Wolfs Den and Karhold as a way to project Stark power on the Bolton’s northern and southern flanks by planting cadet branches in the east of the North. 

In terms of Stark allies? Well, given that the Umbers got a bunch of the Bolton’s northern land, I’d say the Umbers. The Hornwoods are also a good bet. (Which would provide another reason why Ramsay targeted them) The Cerwyns, the Glover, and the Tallharts would also be good bets.