Strava winter map overlay generally shows correctly nordic/cross country trails by parsing the piste:type=nordic from the way regardless of whether it is a dedicated nordic:piste or if it is a nordic trail that goes along a road/trail (e.g. highway=track, highway=path). However, if the piste:type=nordic is on a way tagged highway=footway the trail is not indicated as a nordic trail on strava heatmap. (NB: this is this may well be a mapbox bug and not a strava bug.)
for example, if we look at this location
https://www.strava.com/maps/global-heatmap?sport=All&style=winter&terrain=false&labels=true&poi=true&cPhotos=true&gColor=hot&gOpacity=51#15.52/44.201008/-71.215744
we can see that FR 512 (which is a highway=track) is shown as a cross country ski trail, but Huntsmen’s trail, which has the same piste tags as FR 512 is not. This seems to be because Huntsmen’s Trail is tagged a highway=footway.
Cheers,
Carp
