To feel very weirded out by this encounter

That’s really not nice, and not okay.
When I got out walking especially rural spots I always take a walking stick with me, I find it puts dogs off coming towards you they are much wearier, it sends out a subconscious message also to other people. These days you have to be so careful, and I hate to say it because you should be able to wear noise cancelling earphones but out alone they aren’t a great idea.

No, that is not what's being said, and you know it so stop the manipulation.

Nobody "trains" their dog to sniff crotches, dogs do sniff crotches because they produce pheromones which a dog can read to glean information. Dogs do not do this for kicks.

Responsible owners pull the dog away if it is on the lead, or they apologise, because regardless of how "charming" they find their dogs, they KNOW that crotch sniffing is inappropriate.

The issue here is not the dog.
It is the grinning man that failed to move the dog while it was being inappropriate under his control, so, address your bile towards the gurning man who used an extension of himself to sniff a womans crotch.

It wouldn't have happened with a female owner, or a decent male owner.

You could be right. He could have trained his dog to approach women and sniff their crotches.

Or, he's just another dog owner who can't fathom that no one else wants his dog near them.

How do you know he didn't apologise, if you had noise cancelling headphones in?

I think your instincts are correct.

I’d report to the police. Just in case. The barefoot thing suggests he’s a bit odd. They would probably appreciate being made aware of his antics.

No, he doesnt think his dog is charming. He's using a dog to humiliate a woman.
Aim your barbs in the right direction.

Do you not think the man should have apologised and pulled the dog away, rather than letting it bury its face in her groin and grinning about it?

100% on purpose and getting a kick out of it. I agree with PP he's probably trained the dog to do it. I wouldn't walk that way again for a good while if I were you OP.

Another wanker who thinks his dog is charming and everyone agrees.

To be honest I wouldn't walk that route anymore, particularly with headphones in. He sounds incredibly strange.

Barefoot - eww (and ouch) - that really is odd. I wonder how far he had walked.

I think it's the smirk on his face that's telling - you mention it in your OP so it obviously struck a chord, and your instincts were telling you what his attitude/intention was. A "normal" dog owner would have pulled their dog away, apologised profusely and asked if you were ok. He did none of these things. What actually happened could easily be explained away by him if questioned, but his attitude is the giveaway.
This sort of thing leaves you with an uneasy feeling doesn't it - you feel as though you have been sullied in some way. Ugh, horrible man.

(I had the same feeling when I was trying on a dress in an Oxfam shop years ago, just behind a curtain in the shop, and a man pulled back the curtain "by mistake", said oops sorry, and then sniggered a bit with his mate whilst I was hastily getting dressed again. He just smirked too when I came out - I felt unreasonably furious and grubby in equal measures. I would never try on anything in those circumstances again.)

My BIL and SIL used to have a dog that did this (it's dead now). Every bloody time we visited, it would shove it's head into my crotch or bum, sometimes with slobber everywhere. They always pulled it off quickly, but nevertheless, so annoying!

I agree that the guy is a perv OP, but it does make me a little concerned that you aren't concentrating enough on what is going on around you. You couldn't hear due to headphones, and walking along with your head down, you could easily end up being hit by a vehicle of some sort, or sexually assaulted by someone who you weren't even aware was close to you. I know we shouldn't have to, but I think it makes sense to keep your wits about you when you're out walking alone.

The last time a dog did this to me I was 16 and wearing a skirt and the guy who owned it and his mate hauled it off straight away and apologised (it was not on a lead as it was in its own yard).

So I would say yes, this guy's a perv.

I do remember though, years and years ago before wheelie bins, you had to put the bin bags out at the front of your house for collection, and a neighbour had a dog - a GS I think - that the son of the family used to just let out to wander. That fucking dog ALWAYS ripped my bin bag open and got out my used sanitary towels - no matter how wrapped up they were. It didn't bother with anything like scraps of meat etc which you would have thought it would be more interested in, just my sanpro - SO embarrassing, and there was no other way to dispose of them. So I think they can smell period blood, but that doesn't mean they should be allowed to sniff women's crotches willy nilly. I would have complained to him to get his dog under control. I certainly complained to the neighbour.

Weird. Some men believe the dogs can smell period blood and will seek it out if they have been fed raw meat - had to inform an acquaintance who used this as an ‘excuse’ that I was not in fact bleeding and his dog was just pervy.

Fairly certain he's getting a thrill out of it. Probably trained the dog to do it. Sad pervert.

If you see him again, before he gets near you tell him to keep his dog away from you