It depends, for what reason do you want to remove them? If it's for aesthetic reasons - to give them a "classic tree" shape with a clear stem - then that is just up to you. Just proceed carefully and remove the material over the course of two or three years, if it's a substantial proportion of the whole plant to avoid shock.
If you want to maintain this as a productive orchard then I doubt it will be beneficial to prune out those branches and I suspect they may in fact be a deliberate result of formative pruning from the first few years of these trees lives. If you want to keep these trees as productive as possible then I suggest looking up specific advice for pruning walnut trees, in orchards specifically.
All the normal advice for pruning applies: start by removing the three D's: Dead, Diseased, and Damaged branches. Then remove any branches that are crossing each other and those that are growing inwards.