I am not sure if this is OP. My initial thought is that it is actually UP, but I honestly don't know.
Along with price reduction, Bridge gives +$1 and +1 Buy. Highway gives no special bonus, but it is cantrip. Princess gives +1 Buy and the price reduction is worth $2 instead of just $1. All of these cards cause price reduction as soon as they are played, which allows for cute tricks with cost-caring cards (Remodel, Swindler, Saboteur, Ironworks, etc.) if you play enough of them.
Viaduct doesn't quite work this way (unless you use Black Market) because you play cards before you buy any. So that's one strategic consideration out the window.
How much is Viaduct worth on its own? It does nothing with the first buy. Second buy, costs have been reduced by $1. Third buy, costs have been reduced by $2. If you use all three buys, Viaduct is worth a Gold. Very good, except how often are you going to use three buys?
If you manage to play two Viaducts (including duplicated plays, e.g. with Throne Room), the cost reduction is even better. Hm... now I'm starting to think it might really be OP.
How easy is it get Provinces with Viaduct?Let's see what happens with a simple two-card combo: KC-Viaduct. With just those two cards, you get +6 Buys (7 total) and each Card purchased will reduce cost by a whopping $3.
The thing to note here is that you can spend a couple of early buys on Copper. So let's pretend you only have $2 in hand after playing KC-Viaduct. Very sad! But you buy a Copper... now everything costs $3 less. You could buy a Duchy now, but let's just buy something that's free -- Silver, maybe. Now everything costs $6 less -- oh, you can afford Province now! And actually, after that, all the other Provinces are free as well. Holy smokes. With just two cards (KC-Viaduct) and $2 in hand (easily achieved with a single Silver or any number of support cards) you've snagged yourself 5 Provinces. WOW.
With just a little support (a little more starting cash, Village or some other way to play another Viaduct or two) you could easily take down all 8 Provinces.
So OK, after some thought, I conclude that it is OP. But at first glance it did seem weak.
It might be more reasonable with just a single +Buy, or maybe if it had a "while this is in play" clause (like Highway) so that it can't just destroy everything with a KC.
I really like this concept, by the way. Definitely do more testing with this.