Not Goats-- but something to consider...
Two years ago I wanted to hunt a remote, high elevation area for 16 days with my brother and a friend. I could not get a packer to take us there-- response being "I can't get my mules in there".
I thought I was smart, since I've packed by mule in a few times and also ridden horses for years...
I knew of a seldom used trail about 3/4 of the way up the mountain. I thought would be really smart, genius in fact, rent me up some burros and since they are skinnier, use them to navigate the steep, tight areas where "mules couldn't get". What a cluster. I wasted 3 full hunting days and far too much money on that genius move.
Consider the following very strongly:
Burros have extremely short legs when compared to a mule (and Goats are even shorter), once laden with pannier bags on each side, burros are actually nearly as wide a mule and their panniers hang about 18" off the ground (if that). When trying to lead or drive them up a steep single track trail, they have nowhere near the long legged ground clearance of mule. The burros' saddle bags were far too low to clear stumps, large rocks, logs and willows that were occasionally jammed up on each side of the main trail up the drainage (never mind any small side trails). They hung up EVERYWHERE. Forget about blow-downs- they could not get over them (even low ones). We had one major yard sale when a pannier tore wide open on a rock when our shortest mule dragged it across a sharp edge. We never even made it to the "secret" trail to the remote area. We ended up have to abort our climb up the trail after spending 3 hours dealing with unhappy burros, had to bailing-wire the ripped pannier back together. Went back down the mountain, left the shortest burro there at corral, re-packed the following morning with one less burro then wasted hours driving the mules up to our fall-back, secondary camp site. We had to leave almost a weeks worth of food down the mountain due to lack of the short burro, which meant another trip down/then up the mountain one week later. Wasted another day on that one.
1) Goats are shorter than burros. 2) RE-read number 1
Best of luck!
JL