My dad is a bit the same - not a 'day centre activity' or 'puzzle/games' type of person and loves the garden. I am fortunate in that he will go to a tea room and likes a walk, though he's not good in the cold either. It's this time of year that is the worst, but he takes a real pleasure in just being able to look out in the garden at the birds. I gather from your post that your dad likes the outdoors and maybe he already has a bird feeding station, but if he hasn't I would really recommend setting one up with him. If he no longer has a garden, a simple window feeder that has suckers would do the job, though it takes a while for the birds to get used to it. You could also make your own fat balls using suet and mixed seed - things like that.
I had an idea to make a next box with my dad this year, but he is a bit too far gone to do the carpentry so my partner made the box and I got my dad to help me paint it. (You can buy kits online too, or ready-made boxes you can paint at home). Just another suggestion; it's a matter of finding those little things that they can still do without too much stress and anxiety.
And I agree with one of the other respondents - dementia sufferers don't always agree to things you might suggest, so if you said one day to your dad 'come on, we're going out for a drive' I expect he would go. I often say we're going on a 'magical mystery tour' if it's a horrid day and we can't do much - my dad loves just being driven around looking at things and he often remembers a few things from his past along the way that we can talk about.
If your dad has a bus pass I've been told that a 'carer' can travel free with them, so that may also be an option. My dad lives in Oxfordshire, so I guess it may be not be the case in all counties, so best check that out first.
Other things that may interest him: indoor gardens - I'm thinking botanical gardens with greenhouses (Kew, Eden or nearest botanic if you have one); aquarium; any kind of wildlife centre with animals that need heat! (We live fairly near the Rainforest Centre near Newbury and that's a godsend at this time of year - tropical heat and a lot of interesting things to see).
Also, dvds can be good for keeping them happy for an hour or two. My dad can't follow storylines in films or dramas, but he loves wildlife programmes and dog programmes, so I buy them 2nd hand online and he then has something to watch without having to endure adverts and the daft programmes on the TV.
Anyway, that's a few suggestions. Hope they help.