A steep technical road for 4WD or MTB - highway=path or highway=track?

We have a hilly forest near where I live, which has this pattern of normal roads circling a hill, and “roads” (which are just gaps in the forest) descending a steepest line down the hill:

http://www.openstreetmap.org/#map=17/32.58477/35.02262

These steep “roads” are used by 4WD vehicles and mountain-bikes; one of them is partly an official hiking path.

http://imgur.com/3Cdlnxp

Which value of the “highway” key should I use for marking them?

highway=track? (because it’s used by motorized vehicles)

highway=path? (because it can only be used by special vehicles, and I don’t want these ways to be used for any automatic routing)

If there are several (5-10) of these “roads” in the area, and some of them clearly are not (and I guess cannot be) used by 4WD vehicles, should this influence the value of their “highway” key?

One of these “roads” has a sign “entrance for vehicles is forbidden”; should this influence the value of its “highway” key?

In addition, if I use highway=track (like I think I should), which keys should I add to set them apart from “normal” roads?

highway=track is the correct tags for vehicles that leave separate tyre tracks and highway=path is only suitable for walking hiking, biking, etc and not for 4 or more wheeled vehicles that leave a ‘tracked mark’, though the image you have uploaded could be either and I would be guided by the look of the way where it goes over ground instead of the large rocks. And certainly add surface= tags.
There is a 4WD tag for special road conditions conditions
https://wiki.openstreetmap.org/wiki/Tag:4wd_only%3Dyes
There is also the track type
https://wiki.openstreetmap.org/wiki/Key:tracktype
Also the Australian tagging guidelines may be useful info
https://wiki.openstreetmap.org/wiki/Australian_Tagging_Guidelines#Unsealed_and_4wd_Roads_.28Dirt.2C_Gravel.2C_Formed.2C_etc.29
You could use the access tags to define the ones where vehicles are forbidden/allowed but I don’t think this should influence the highway tag (in most cases?).
https://wiki.openstreetmap.org/wiki/Key:access

Agreed, if it is possible to take a car and it does happen from time to time, it should at least be a track. In less developped countries, a road like this might actually connect major towns, so in that case it could even be rightfully tagged as secondary or even primary.

To make the suggestions in the replies above more concrete:

highway=track (as suggested by the users above)
motor_vehicle=no (where it’s forbidden by a sign)
surface=unpaved (to override the default “paved”)

Also, after some digging, I found the following that seems appropriate:
smoothness=very_horrible

I was unaware that the default surface of a track was “paved”. The wiki at https://wiki.openstreetmap.org/wiki/Tag:highway%3Dtrack says:

“This tag represents roads for mostly agricultural use, forest tracks etc.; usually unpaved (unsealed) but may occasionally apply to paved tracks as well, that are suitable for two-track vehicles, such as tractors or jeeps.”

In the mapping I’ve done I have left off the surface tag unless it was paved.