Having said that, I'd have been tempted in this set to play for Alchemists with this set, running off one Woodcutter, two potions, money, and as many alchemists as you can buy. Its not as fast as the most efficient garden strategies, but then I don't think the most efficient garden strategies were available this game.
(...)
Much easier to go for the Alchemist route.
Gardens was definitely the right call here, so by making that choice you definitely played better than your opponent, I say.
Best of 5 gogo.
Seriously, I think some of the advice given, while well-meaning, will be quite lost on the OP. So he asks on this board "did I play well or was I just lucky", to which "Workshop is a better enabler than Woodcutter for Gardens" doesn't really fly does it? Because while we vets know how Woodcutter/Gardens works, how to play it, and how it isn't on an elite level of Gardens enabler, the OP's game suggests that he doesn't. (e.g. open Woodcutter/Garden and then buy Woodcutter on $5, that can't be right!)
To the OP, I'd say this: when going for a Gardens strategy, the advice "don't buy copper" should generally be disregarded; usually Coppers are bad because they stop you drawing $8 in one hand, but in a Gardens strategy you shouldn't be doing that.
Each Gardens enabler plays differently, and you need to be comfortable with how they function. While most seek to empty out the three piles of Gardens, Estates, and itself, some enable you to grab a few Duchies along the way (notably Ironworks) while some others usually can't. Also, for the $3 enablers of Woodcutter and Workshop, you usually don't open Garden/X but rather X/X and then go for the Gardens Turn 3 onwards (or even later). "Even-ing out" your enabler and Gardens purchases is usually a bad idea.
Trader/Gardens is a whole new story, because not only does your enabler cost $4 (which means you can't open with 2 Traders), you don't usually want to empty the Trader pile (although Silver(!) pile is possible especially if your opponent also has Trader). Also, a high concentration of Silvers means that not only can you buy some Provinces, you might even find after a few turns that you can actually get your fair share of Provinces even if you lose the Gardens-split? I think very few of us are expert in Trader/Gardens at this moment and some experimentation is still possible.
But back to Woodcutter/Gardens, which is what you played: primarily you want a few Woodcutters to start. Then you start greening by buying up nothing but Gardens (Coppers with extra buys) until the Gardens deck is exhausted. When that is done, you evaluate to see whether rushing out the Estates + one other pile wins you the game, or whether you need to actually switch out and try for a few Duchies too. This makes a difference when you have $5 and two buys: should it be Woodcuter + Estate, Estate + Estate, or Duchy + Copper? The decision depends on how well your opponent's deck is going, whether he is going for the same strategy, whether he has the capability to end the game soon, etc.
But generally you don't have the luxury of dipping into other stacks like Walled Villages or Envoys. As explained by other posters, they are near useless in any dedicated Gardens deck (other than adding to deck size), and simply giving your opponent more time to get Golds, Provinces and Duchies while you are unable to end the game on 3-piles.
Whatever strategy you do adopt, try to play it to the best of its ability first and not get into the finer points of whether Woodcutter/Gardens or Trader/Gardens or Woodcutter/Trader/Gardens is better. Once you can play all 3 of the strategies competently, you will be able to form your own opinion on the matter.