Do you think my cousin was rude when I wished him a “Happy Veterans Day”?

I mean obviously it wasn't the politest response, but to an extent, I agree with Lucyy. After going off and serving his country, and very likely experiencing trauma, I think he has a right to be a bit snippy when that trauma is brought up. Its not fair to call him ungrateful for that when he served your country. I think a little bit of empathy here is needed on your part if I'm honest. After all he has done, there's no reason to hold a grudge against him for something that only took you maybe 20 seconds to type out. Everyone is entitled to a bad day, and a veteran having to be reminded of the time that he spent serving is absolutely enough to make it a bad day. And veterans are also definitely entitled to PTSD responses when that's brought up. I don't think it's something he should have to apologize for in order for you to not hold it against him. My Grandpa was in the military, and hearing a loud noise can trigger his PTSD so badly that he can have the whole day be ruined for him, or even a couple of days. That reminder for them can be way more inconvenient that it is for you to just not get the response that you wanted to a text. I would just let it go if I were you, and have a bit of empathy for his situation.