Hi Lori, a big rug right where they're coming in and a firm command of sit the minute they get in the house is vital. After that I always keep a towel handy. If they're really bad they make hypoallergenic wet wipes that work great.
Here are some great ideas: https://www.installitdirect.com/learn/how-to-keep-mud-out-of-the-house-during-rainy-weather/
You could also get some dog booties to keep them clean and unharmed by ice, salts and other stuff. All our sled dogs wore them... https://www.google.com/search?client=opera&q=winter+dog+booties&sourceid=opera&ie=UTF-8&oe=UTF-8 we used to make them with a heavy nylon fabric and velco.
Bucket of water by the door. Change after every outdoor event. My dogs refuse to wear booties. Just swish their paws in the water, then dry off.