Just my two cents here:
It mainly depends on how you define “Pay to win”. In general, I think it’s more useful to evaluate which mechanics are and are not present in the game.
This will be focussed on Constructed mode, as Arena isn’t influenced by purchases and Battlegrounds only has a minor influence.
Yes, the BG Pass arguably gives an advantage, but if you mainly play BG over constructed, it shouldn’t be too hard to save up the necessary gold and, if you are really committed to playing both BG and constructed as FTP you could easily run a constructed-focussed account on one region server and a BG-focussed account on another, thereby having two streams of gold.
On to the Constructed issues
- 1) Does HS feature a mechanic where money can directly be poured in game to yield an advantage?
No. By this I mean that one cannot increase the power of their deck by simply spending more money, nor are there “premium” versions of cards that are only accessible with high expenses. This contrasts with other games where you can “upgrade” your units/heroes/whatever by spending resources, thereby giving an advantage to those who can use money to gain more of those resources.
In HS, Mutanus is the same, whether you opened it, crafted it or purchased it. There is no mechanical difference between a regular, golden or diamond version of any card.
Once a player’s deck list is “complete”, they cannot invest more resources to further improve their deck’s power/win rate.
- 2) Are there game elements which cannot be acquired without spending money?
No. Aside from cosmetics and card backs (which have no in-game effect), there are no cards which cannot be acquired through opening packs and/or crafting. This was not always the case, but now even cards from the older adventures are craftable.
- 3) Can making real-money purchases provide an advantage?
Yes. Cash purchases will inevitably increase the speed with which you fill your collection and allow you to potentially have the resources to build several decks, thereby more easily adapting to shifts in the meta.
In conclusion
Paying money will allow you to save time, but, once a deck list has been completed (which can be done as FTP) the paying player will not have any advantage over the FTP player in a given match.
Does this make HS P2W? As I said at the start of the wall of text, it depends on how you define P2W.
If (like me btw) you define it as “a game is P2W if the paying player has advantages unavailable to F2P players and/or will always be mechanically advantaged over the free player”, then no.
If you define it as “any game where real money purchases give any kind of benefit whatsoever”, then yes, like any game with non-cosmetic microtransactions, HS is P2W. If you’ll allow the strawman though, by this definition, basketball is P2W, since someone who can pay for sneakers has an advantage over someone who has to play barefoot.