You could take him swimming?
Or set up assault courses round the house. Make a tunnel by draping a rug or sheet over some chairs perhaps. Practise climbing the stairs together.
Not sure where you're based (and whether you mean "cold" in the uk sense or North American sense
) but maybe invest in some good winter waterproof outdoor clothes and boots for the two of you so you can get out whatever the weather?
Does he like music? Would he enjoy dancing about with scarves/bubbles/shakers/bells... Or a rhyme time session?