Yes...and no.

From what I understand, most items will have a legal owner, and certain things, like a land deed for example, will generally belong to the whoever is the head of your house. That'll probably be one of your parents, so, when it comes to your control over those assets, the limiting factor will probably be that person. If the character doesn't trust you or just dislikes you, it is quite possible that you won't have 'legal' access to any of those things. Caspian once mentioned, for example, that in order to inherit your family's wares, you would have to be in your parents' favour–enough, at least, to be named the heir–or they may simply relinquish their land, money, livestock, etcetera to another child or their reigning count.

There is a little control when choosing a family to start out in, but they will generally be within the same class as you need Story Points to pick characters with more assets, power, and higher levels of fame.