In the depths of Moria, the mount of choice is the goat - indeed, it is the only mount available. An extensive and reasonably well-placed network of goat stables allows normal and even (after you achieve a high enough status) some rapid goat travel to most of the points of interest in the mines. However, players can also acquire their very own goat from the Iron Garrison Miners: a rather slow Tame Redhorn Goat costs 1g, 255s and requires Friend standing, but if you've achieved Kindred standing and have a spare 6g, 24s, you can acquire the faster Nimble Redhorn Goat. Actually, this is pretty much the only reason for striving to reach Kindred with the Miners.
Even by current inflationary standards, 6g is nothing to be sneezed at for the average player. Is it worth the effort and expense? Well, it's an oddly attractive beast, has a cute miner's lantern swinging from the back of the saddle, and, unlike its goat express cousins, it doesn't suddenly spin round and round whenever it gets confused about routing... but to be honest, you won't be using it very much. The problem is that it is extremely vulnerable to attack, and can be brought down by about three hits, or even a dirty look and a spit. Which is about all the standard LOTRO horse or pony can take, too, except for the fact that out on the surface, if you stick to the roads you will usually get home safely. In Moria, however, the passages are inevitably narrow, there are endless choke points and little or no room for evasive manoeuvres and, above all, the mines are positively crawling with orcs and other nasties. As a result, you will rarely stay in the saddle for more than a few minutes or even seconds, with the added bonus that when you do come off, you are welcomed by all the mobs you've pulled along the way.
There are of course a few routes in Moria which are pretty much free of lurking enemies: the Wide Halls and Broad Way in Zelem-melek, and the long winding passage from the Great Delving to the 21st Hall, for three. On balance, however, the Moria goat remains a luxury for the rich or the obsessive completist; for everyone else, swift travel and the goat express service are definitely the better bet.