I assume you know this already but I’ll put it out there because I think it should be said regardless: not all stallions standing in Europe will offer frozen. Some stallions just don’t freeze well. Other times it may come down to the quarantine requirements that clash with a rigorous competition schedule.
I’m operating on the assumption the stallion owners are marketing frozen (and you just need to figure out how to get it here).
One really valuable resource would probably be the frozen semen brokers in North America. Based on how long many of them have been in business, they’d have more than enough experience and insight to help guide you if you can get a hold of them and they’re willing to speak with you.
As far as storing semen, what I am familiar with is pretty split between storing it at a vet’s (the big repro vets in our area have frozen tanks and you pay them to store frozen for you) or having your own tank you maintain. Depending on how much frozen you anticipate keeping/maintaining, one may be more cost effective than the other. That said, regardless of which method you use follow best practices and document everything! (Number of straws, labelling on straws, dates, etc.) There can and have been slip-ups (wrong straws sent, fewer straws than a dose should be, mis-reading straws, etc) so always do your best to protect yourself against those sorts of things.
