In Scrolls, it seems like Trials can only be completed once for gold. Do they reset after some time for the ability to earn additional gold, a la daily quests in WoW, or once I finish them is my only option to earn by playing Quick Match?
No, they don't reset. Although this may change in the future, when you first download and play the game, I recall reading a specific message that states that upon the first, initial completion of a Trial, you are given a reward. After that, you can continue to play the trials but you will not receive rewards for winning the trials.
If you would like to earn additional gold, just play Quick Matches or player-to-player games.
UPDATE - 1-30-2015
According to user Mike R, in the comments below, the Trials system has been updated. For future-history, formerly there was a list of trials ranging from Easy, to Medium, to Hard. Each trial provided a reward upon the first time it was completed.
Today, this still holds true but (again, according to Mike R) a short-list of trials are refreshed each day. You can earn the rewards once per day.
RLH's answer was correct at the time it was given, but is now partially obsolete due to subsequent patches.
There are now daily trials, one each for Easy, Medium, and Hard difficulty. These can be completed once a day each for reward.
The original trials are still only completable once each for reward, and do not reset.