The more I think about this the less I like my own idea. It feels like re-hashing Assyria with a prod/faith focus instead of sci/culture. I really like the idea of this being a barbarian civ which gets culturally dominated, but remains very militarily threatening.
UA: All units can use roads in enemy territory. +10% combat strength for every level of influence the opposing civilization has against the Goths. Capturing any city for the first time reduces the cost of subsequent social policies by 2% (up to 20% max) and capturing a foreign

Capital triggers a

Golden Age and grants a free social policy.
Would it be difficult to have the cost of social policies reduced by conquering cities? Alternatively, city capture could reduce only the
next social policy by 25%. I bet a flat reduction in policy cost is easier to code though. Having a mechanic like this would incentivize the player to neglect culture for a military edge and help mitigate the loss of policies. You'd just have to contend with tiny borders.
It looks like this civ is dual-focused on faith and military, so I think it would be fine. I don't see much issue with adding military-focused bonuses to a temple though, especially given that Gothic paganism worshipped the AEsir, an overtly militaristic pantheon. Regardless, I think the barracks is a little TOO early, as the goths are definitely
not an ancient era civ. You're the guy coding though, I won't complain if you go with your gut. If you prefer the barracks you could do something like this:
Hov - replaces barracks
+1 production
+2 faith
+1 prod & +1 faith from horses, cattle, sheep, and deer
+10% production towards land units
+20 unit XP
-20% crime modifier
+2 unit supply cap
no maintenance
unlocked at construction (instead of military theory. This puts it in the prerequisite tech line for the UU)
If it's a barracks replacement, you could also do a unique promotion for units built in that city:
Blessing of Donar (production in capital from pillaged tiles equal to gold, +10% combat strength vs. barbarians)
As I said, you the boss; I'm just the non-coding pleb. I'll be happy with whatever you decide on.
Edit: A note on the historical period of the Goths.
The earliest recorded account of the Goths is of their displacement of Germanic peoples southward, which precipitated the Marcomannic Wars in 160 AD. They sacked Histria in 238 and lost badly at Naissus in 268.
The beginning of Medieval era in western culture is traditionally demarcated by the fall of Western Rome in the 5th century. The sack of Rome by Alaric was in 410, and the entire Italian peninsula was an Ostrogothic kingdom starting in 493. The Visigoths continued west and set up various kingdoms in Iberia starting in 418, until their eventual conquest by the Moors. Gothic culture remained, however, and Spanish royalty trace their lineage to the preceding Gothic states, which were re-established after the Reconquista.
So TL;DR, the Goths are the very definition of an early medieval civ, but late classical can fit in a pinch. Given that context, the hov being a replacement for later techs like temple or stable isn't far off, except that the hov harkens back to their pre-romanized culture.