There is nothing in the spell that suggests that the mount resizes, and it specifically says the mount gets the features described in the peryton's description. Furthermore, whatever the peryton's description says should apply to the summoned mount.
You might want to have a discussion with your GM about how this will work in your specific game.
Regarding re-sizing, while that might make *some** sense, that's not what the spell says. There's a fundamental rule in D&D that spells do only what they say they do.
You can decide it seems reasonable to you that the peryton would be large, and maybe that makes sense to you. Depending on your GM, it might or might not be true. The rules don't provide an answer other than a peryton is medium. A great way to find out is to discuss it with your GM and then try it. To me, the rules say it's medium, then it's medium. A fundamental rule in D&D is that the GM describes the environment, the players describe what they want to do, the GM describes the results of their actions. So try it. Another fundamental rule is "rulings, not rules". The rules explicitly say the GM can interpret, change, or ignore the rules as he or she sees fit.
Good luck with that peryton. Have you read that description? Scary beastie.