If you can do the refinishing of this door depends on your experience with refinishing wood and your confidence. I think that anybody can do this if they use common sense and don't rush. I guess what I'm saying is; Do you really want to do this or would you rather put the responsibility on someone else's shoulders? If you say "yes" to just one of these questions, consider hiring a pro to do the work for you.
If you decide to do the refinishing yourself here is a list of products I would use;
1) The Paint Stripper – I would try Peel Away 7 first, using their paper to keep the stripper moist and working. This is a good all around paint and varnish stripper that isn't too caustic. If for some reason the Peel Away doesn't work, use Jasco/Bix Varnish & Stain Remover. This stuff is caustic and will remove any stubborn finish.
Always start with the more friendly paint stripper first.
2) Sanding – Even the best paint strippers will leave some color behind. To remove this discoloration and produce a smooth surface I like to use Norton 3X High Performance Sandpaper and a good palm sander.
Start with either 100 or 120 grit paper. This will chew through the wood very quickly and remove the discoloration. Now progress to 150 grit then 180 grit. The finer sandpaper is necessary for a blotch free door after it is stained.
3) The Wood Stain – I like the Old Masters line of stains. They have a very good wiping stain that is easy to use. You might have to use a prestain conditioner. This depends on the wood species. Generally, use a stain conditioner on soft woods.
4) The Finish – You have a lot of choices on the market. For your area I would use McCloskey Man-O-War marine spar varnish. This stuff is tough when fully cured. Plan on two separate coats with a light sanding and tacking between the coats.