Managing poop (particularly in winter)

[gte510i]

Here is our current set-up:
Coop: top level, with roosting bars, nesting boxes, feeders, and straw.
Lower lever: dirt/sand, waterer, grit, oyster shells and a swing.

Chickens have open access to a pasture with a mobile electric fence.

In winter, they mainly stay in the building, maybe venturing a 7 foot radius out in snow.

Two problems, as snow melts, we have nasty mud with a a whole winter's worth of poop that had frozen solid.

2) the sand/dirt bottom has collected a lot of fallen straw/poop/dripped and frozen water

When it thaws I have the joy of digging all of that up. It's a matted smelly mess. Sand can't go in the compost pile. It's also the grossest thing I have ever done.
How do y'all handle winter coop management? My deep litter works fine I. The roosting area.

 

[aart]

Do deep litter in the run area too.....and anywhere they roam that is plain dirt/poop/wet. As the snow melts, keep adding deep litter type materials.