Wood floors and heated floors

I had the brilliant idea of putting in all new wood floors! Wood floors look so sleek plus classy–I also dislike vacuuming plus cleaning spills off rugs. Wood floors in the summer time are great. I only need to mop every so often plus the floors look attractive. Yet wood flooring is horrible in the winter,! The floors are always dusty due to my gas furnace device! Since my gas furnace system is on plus running, dust gets into the air quality. The dust then settles on the floors for myself and others to wash every week. The wood floors are also super cold. The frosty air leaks into the apartment plus the wood feels even colder. I can’t be barefoot in the winter. I have to wear socks plus usually I put on slippers too. The gas furnace does not do anything to help the frosty floor issue either. All the heated air rises to my ceiling, the flooring never gets touched. I have looked into this plus there is really nothing I can do. What I could do is remove my furnace plus get heated flooring installed. The heating would stay at the flooring level, plus really warm the wood floors. The wood unquestionably would help the gas furnace suppose warmer. I can’t do this though. In order to have radiant floors, the existing floors have to be ripped up. I just bought the wood flooring, I can’t destroy it in the heating replacement process. I loathe having frosty feet all of the time. So I am thinking about putting a rug over my brand new floors due to the cold.