Personally I don't count trees that have been planted (non-native or otherwise) whether that be a forestry plantation, amenity trees in parklands or planted trees in gardens. In fact I wouldn't count any plant at all if I know it was planted. But I do count self-seeded trees such as Sitka, Lodgepole Pine, various larches etc. I live on Skye and Sitka is (very worryingly) one of the commonest trees I see across the landscape. The original plantations have often been harvested, but the seedlings survive very well and many are now of cone-bearing age and so the process repeats. Same goes for introduced Scots Pine which, along with the non-native Lodgepole Pine, make up the remaining bulk of conifers I encounter on here on Skye. All completely wild, established, reproducing and hence countable.
I have also spent time wandering through old arboretums in Surrey and Hampshire, specifically searching for 'tickable' self-seeded non-native ornamentals. It's a bit daft I suppose, but good fun trying to key through an unfamiliar conifer.
Full disclosure, I'll happily count any plant that has successfully jumped the garden/arboretum fence, so my rules are probably looser than those of some other listers here.
