Our cows water out of automatic waterers. Our heifers that we keep and the bulls sometimes water out of springs though.
The muckier areas should freeze they always do around here and the only thing that stays open is where the spring comes out of the ground. The cows will pack down a trail as it is freezing and have a path that is usually fairly smooth. Although closer to the actual source of water it can still be bumpy and when those bumps freeze there can be some sprained legs if they are the fighting type so you might want to take that into consideration.
Some of our springs don't stay open all year but they are the ones that look more like water holes - fairly smooth until you hit the water. Those ones I have to open so I usually just fill up buckets for the cattle, now that I have a house down here, it's easier. The springs that the cows have a hard time walking to all summer usually stay open all winter. Just keep an eye on it to make sure it doesn't freeze. If you decide to use it for the winter go out now and make sure you know where the water actually comes out of the ground just in case you have to open it.
We have never had calves in the fields with our boggy springs until they were older. How far do the cows sink? Any more than knee deep?
I'm not sure how far away your spring is from the furthest point of mud but you could try getting out a bobcat and just digging it out. If you dig out to the edge of the mud as low as where the spring comes up you will turn it into a waterhole. If you have to go to far from the source of the spring though you can have a problem with the water freezing and then the cows are walking on a skating rink to get a drink. That can be helped by putting straw into the water as it freezes though making it less slippery. You may have to dig it out every few years though.
Another method is to put in a culvert(s) and build an actual road to the main source of the spring. That can be a bit more tricky and it depends on the ground around the spring and how often the source moves.
It's hard to tell you what to do not seeing the spring. Sorry I am not being more help.
DON'T let your cattle just eat snow. Some of our neighbours do that and it drives me nuts!
A cow has to eat
a lot of snow before she will get her daily water requirements. Their rumens do not function well if they do not get sufficient water. You will end up not only with a colder cow as mentioned above but you will also end up with cows who are not healthy. Body condition will not be as good, the calves won't do as well, more problems with milking, and more calving problems in general. Besides the fact your cows will be thirsty. We are raising these animals to eat but we have a responsibility to be humane in the process.
Be thankful you just got rain. We got our first dump of snow. :roll: I am NOT ready for winter, the cows are all depressed. The only one who is happy is the dog - she's a Newfoundland and is so excited that she has both snow and the river to play in. Pitiful.