nevw
(Nevw)
6
This link may help to decide if you have used the most suitable tag
http://wiki.openstreetmap.org/wiki/Key:highway
I expect that some of the trails you are seeing nearby are tagged as tracks, which means that a vehicle can traverse them, like 4wd or forestry vehicle tracks in forests.
Your ways are tagged as footways which means a single track for foot traffic instead of a wheeled track that can accommodate vehicles as well. Brideways for horses and cycle suitable ways render differently on most maps too.
At the openstreetmap.org map, on the right side under the ‘layers’ tag (stack of books icon), you can select ‘Map data’, and then select each way to see the tags used. Zoom in closeish when doing this as it memory hungry.