Sorry I should have said - the gateway is a funny angle and we can't get a vehicle in without taking post and rail up. Garden roller might be an idea - I'm just worried about it freezing in its current state!
if it is the gateways then you could dig the mud off and put some stone/rubble down which would solve the problem for the future.
For small paddocks something has to tow a roller, the choices are quad, horse, normal size tractor but 4wd tractors often leave more mess than they resolve or a compact tractor which has a much lighter footprint. A case of whatever is available.
For the funny gateway angle can that be resolved to improve access? one alternative would be to move the post and change the angle, another would be to put the gatepost into a socket and make the rails into slip rails.That way if you wanted vehicle access you simply slide the rails out, lift the post out of the socket and you have nice gateway.
We have done that on several gates where we need wider access.