What tag should I use for this barrier?

Looks like brash (cut twigs and small logs left over from cutting wood). Often left as piles after woodland work to provide habitat and avoid burning. In nature reserves brash is often placed as a barrier to prevent people (and particularly dogs from straying from the path into areas of conservation importance.

This does not particularly look like a properly laid windrow (or dead hedge) which will typically be made by hammering sturdy cut branches into the ground to provide a frame for interleaving smaller twigs etc. Although I'm more used to calling them windrows, dead hedge would be a term more likely to be instantly meaningful for most people.

I'd therefore be tempted to suggest two values of barrier: brash_pile for a jumble of dead wood and dead_hedge for something with more structure & longer. Depending on circumstance the former is likely to be more impermanent than the latter.

barrier=debris might be appropriate here. I think it is typically used more for rubble, but this seems to meet the general description.