Hmm. At first I thought, "how bad could it be to send a simple happy birthday text?" but I see Zap's point. I think a lot depends on where you both are emotionally. If either one of you might be construing more into a message than a simple "I'm thinking of you on your birthday" (or the resulting responses or lack thereof) then maybe it's better left unsaid.
It's so hard for me to say, because the longest relationship I ever had before I met my husband was two years, and that was when I was barely into my 20s. I definitely lacked the emotional maturity to have casual contact with my ex back then, but it may be very different for you.
I think you need to be really honest with yourself about your motivations and whether you're still feeling raw enough that it's better to avoid contact. If both you and he are capable of viewing a text as a simple HBD wish and nothing more, then maybe it would do no harm.
Either way, good luck to you. I know this is a hard time of year when you've experienced such a loss.