Any bedding you put down in winter will get wet. Depending on the soil type you have - ie does it drain well, I would prefer to put a sub base down of something like crushed concrete and then put good quality mats on it.
However, I live in a heavy clay soil area, so nothing would work for me. Your horses will probably only use the field shelter for a wind break anyway, so it doesn't much matter what does inside it.
I put rubber mats down in mine and a normal shavings bed...I have used it as a stable in the winter before now and it has been fine. Now it is used as a shelter that my horse goes in and out of as he pleases.
i have a earth floor in 1 of my stables and i just deep litter it right up to the door, drains well and easy to manage. have a friend who put mats in hers with normal bed on top and that also seems to work well although they move a bit.
we have a wood man near us that gives us the barkof the trees that he deals with - works quite well - is better after a couple of days when it has broken down slightly and its free!!!!
A yard i used to work at had earth floors in the stables and we just had a deep straw bed down on it, but the ground was chalky so it drained really well
i just have mayomats (rubber foam mats) in all mine, and skip out 2x daily, it stays totally dry in there and i know the horses' legs and feet can dry out completely = no mud fever.
My shelters are on sandy soil, I put down about 8" of shavings at the beginning of summer when I scrape them out before the fly season, and they stay dry all year round. I do skip them out though, and I don't feed in them at all.