OSM does have that data, and I've noticed that mapy.cz takes it into account. There are sac_scale [1] and smoothness keys [2]

1. https://wiki.openstreetmap.org/wiki/Key:sac_scale

2. https://wiki.openstreetmap.org/wiki/Key:smoothness

sac seems a little too broad to me; most trails would be level 2 or below, without communicating much more than a simple elevation profile already gives you.