Back in my Exmoor smallholding days, we found that a large covered area around the hen house, under which we spread barked chippings, with straw as they got nearer the house (which didn’t get wet and soggy too quickly as that area was covered) worked really well.
Over a winter, the bark would gradually mulch down, so in spring we could lift the cover and move the house, or move the hens to a different run, and let that winter’s bark and straw mulch in and grass grow on it again.
In a very muddy winter we did need to spread more barked chippings, but I don’t remember having to do it more than once or twice.
When I say ‘barked chippings’, these were a cross between woodchip and bark. Similar size to bark, but not just bark. They worked better than either bark (too soft, and sank in too quickly) or plain woodchip (too small, disappeared equally quickly.). I’m not sure what is the correct term for them. If you can’t find any, I expect a good layer of woodchip with a good layer of bark on top would probably have a similar effect, but would expect to need to replenish the outer edges more often through the winter.