Every dachshund owner I know (and I know several) shovels the yard clear of snow and puts a series of overhead electric heater up so the poor little things can do what they need to do in comfort. During snowy or rainy weather they protect the poor little darling with an umbrella. Daisy Gnedddenhutten was electrocuted last winter when the umbrella she was carrying over her Precious Pepper touched the heating elements of an overhead electric heater; Precious Pepper wouldn't go out again for a couple of hours after that tragedy.

I'm not saying that you should go so far as to electrocute yourself for dachshunds, LH, but certainly you must have the dog's "grounds" arranged as above and so do be careful carrying the umbrella.