I hate mud and have put up with it over 40 yrs seen and done about everything and have not found a really good solution to it.  Reject lime works pretty good as it is cheap and when it gets hauled out to crop fields might actually do some good someday.  Have used it in about every situation possible from around mineral feeders, to areas for bale rings. Recently put in a tire tank with geo fabric and it is holding up nicely.

Some 10 maybe 20 yrs ago I actually worked on an experimental Equip plan for a Winter Feed Station with NRCS of which we dropped and never completed the application.  It was a road threw the pasture with a cul de sac at the end to turn around it would have included large amount of geo fabric and been pretty wide to allow feeding on it.(This is back when fabric was new)  We needed somehow to get the tractor and feed out and turned around.  This was for 100 cows that could come and go to the pad just for eating and loafing in a 30 acre calving area. Wish today we would have gone on and tried it as I am to old now to justify the expense. (Part of the problem was they would still stomp out the area coming and going to the pad)  Kinda like what happens with concrete.  This was only to be used in mud conditions.

We presently have three feed paths that get used everyday where the cows have waste 50% of the hay in this Missouri slop again.  These areas never got healed up from previous March Mud, actually better this year than last so far. The hay build up get solid enough to support the tractor that unrolls the hay with a hydraulic spin off style unroller. We have had it for 25 years.    I would be embarrassed to post pictures how bad it is.  Old saying is you have to feed the mud.  Unrolling hay is the only real way to help a large quantity of babies under 30 day of age.  130 cows calving in 60 days that will move out to summer pasture will ruin a large area.  Lucky we are cursed with Fescue, one does not feel near as bad tromping it into the mud.  It cheap bedding. Cows and calves can move out of the feed areas but one would be surprised how they stay on the packed in hay paths.  This area has had the best soil you could ask for hauled out by a scraper to row crop field twice over the years.  Serious remove a foot of compost off 5 acres is a lot of compose top soil.

My complement to littlejo in thread below as he may have added to my plan, what I will call a safe zone for babies. I have a pond electric fenced off that have watch the calves go under the electric fence wire and lay in the tall grass on the pond dam.  Modifying what he said I could secure an area near my feed area just for calves doing the same with an electric fenced off area.  They would come and go. Have a permanent electric fence, never fall graze it and stockpile just that area for the calves safe zone. Would not need to be very wide even. 30 ft maybe.   I know they will use it because we have one and really did not appreciate it, for what it was doing.  I cursed it cause if the pond is frozen afraid I would have a baby out on the ice some day. Been there done that its a long story for another day. (This area is a smaller herd of 20 first calf heifer pairs where the pond dam get used as a safe zone)