I currently use OSRM for the routing in my apps. This works well for car/truck routing. However, I have an upcoming project that requires routing on hiking trails as well. Are there any available solutions? If not, would it be feasible to use osrm and add the trails manually to osm? any other suggestions?
You can use OSRM for this purpose but you will require a hiking profile. The OSRM demo instance has just a car profile and won't do foot routing. However that's a limitation of this particular OSRM instance and not of the underlying OSM data.
Alternatively just use a different online router. There are lots of different OSM-based routers available, many of the support foot routing.
You can also search for official hiking trails in OSM. waymarkedtrails.org is a great OSM-based source for all kinds of trails (hiking, cycling, mtb, riding, ...) and offers GPX downloads.