Just a word of warning... please don't let him go bare foot.

My DS is 20 months and a few months ago walked bare foot on pavers. They were hot, extremely hot. So hot they burnt and blistered his poor little feet and he had to have them dressed and bandaged for days. He barely stepped on them as well...

I find even at 20 months my DS understands options. I always give him pre warning for things. Ie if you're going for a walk say so half an hour before "We're going for a walk and you need to wear your shoes." Give him the choice like someone else suggested and ease him into the idea slowly rather then pouncing it on him IYKWIM. If he says no then like Cailin suggested, don't go for the walk. He will understand and he will put them on.

Do the same with the hat. Does he like any particular show? Could you get a Thomas hat or a Wiggles hat he might like? Do you wear a hat when you're out as well? Can you put your hats on together?

Good luck with it. I hope you find the solution soon.