Being a regular Lordswood rider, I know that there’s some really miserable dog walkers there (and some nice ones).
I always slow to a crawl, aknowledge them politely, thank them (not sure what for, but it’s the British thing to do), maybe stop and pet the dog briefly to show I’m friendly… Most walkers seem to appreciate this but some still seem to believe the woods belong to them.
Lordswood’s Horseman’s trail as the OP stated is not actually all official footpath (depending which bit you met her on).
The run down the side of the golf course (popular with dog walkers) isn’t an official footpath at all and the land within the main part of Lordswood itself is all just “public access land”…
We should all be polite, courteous and considerate to each other and then just accept that some people are just miserable buggers, whatever you do…