You are right to be concerned about the conflict in your marriage created by differing opinions on the dogs and their care, Evelyn. Pets can become a battle ground for other tensions. The good news is that solving the problem created by the dogs can give your marriage a great beginning, and enhance your confidence in each other.
You inquired about the well being of your husband's two dogs if they are required to spend more of their time outside the house. In all probability, the dogs would adjust to this change. The more difficult problem for you, Evelyn, is your husband's reaction. He is strongly identified with the dogs, and may very well feel that they are a part of his family. If he feels you are “rejecting” them, he may take that personally and feel partially rejected by you.
I suggest that you and your husband work with a dog trainer who can demonstrate to your husband that the dogs are really fine outside. He will need to see this with his own eyes. You can also show him your willingness to compromise. Are there ways you could rearrange the house so the dogs’ presence is less disruptive to you? For example, establish a small “mud room” where the dogs can stay until their paws are dry.