Ours aren't too bad despite almost double the average summer rainfall up here (it's kunekune though so not as much rooting to deal with
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Moving them regularly helps - we used to have two pens for weaners they got about 6 weeks at a time on each. Solid ground around feed/water areas helps - either under trees so the roots provide stability or get some old paving slabs and bed them in to the soft mud. Keep the pigs off until they 'set' and they're pretty unmovable.
Deep, cold mud for extended periods of time can lead to arthritis, but pigs for the freezer won't be around long enough for it to affect them. Breeding stock should be kept on dry ground (or brought in) to ensure long breeding lives.
The real problem with mud and growing weaners is your safety... As they get bigger and the mud gets worse, there's more chance of you getting stuck/knocked over - it's definitely worth having some solid footing. Ask me how I know