This is why people try to have their calving season while there is snow on the ground.
Could be for some. Yes mud and wet conditions can certainly affect and increase the probability, but here there is likely not to be snow on the ground generally for any long length of time. An average winter will yield two maybe 3 measurable snows that are likely to be gone within 1-3 days. There can be longer cold fronts with heavier snow amounts that keep snow on for 2-3 weeks at a time but not every year. There can also be a very rare winter where little to no measurable snow falls.
Most of our winter precipitation is rain which makes for mud and lots of it.
Around here most people start calving in late February-March, when the likelihood of significant snow is decreased, some calve in or through April
The consensus is to avoid the extremes calving in December-January and through mid February are more problematic as is later in May-August for other reasons, heat and flies.
I would say most calves around here are born either in March or September.
Infected navels can happen during any time under the right or I reckon wrong conditions.
Being born in a clean dry sanitary pasture is in my mind the best conditions.
I've found that oftentimes calves born up in a barn or brought to the barn shortly after birth due to cold snow or rain conditions can increase the likelihood of navel infections. I always iodine navels of barn calves as soon as possible, and like go get them out of the barn as soon as possible too.
I believe flies can cause problems to.
Another thing that I believe can lead to infection that can happen is if the navel cord breaks off too close to the body at birth or if the cow licks it too vigorously and it tears off to close it leaves an opening for germs and or flies to cause trouble.
It's just something that has to be watched for in young calves in the same sense of watching for signs of scouring or other common ills at affect calves.