It's been a while since we talked. I hope you're well and that your day's really nice.

Yes, being a zombie is suffering. The pain is dull and hopeless, all the more horrible for being inarticulate. The mind is wild and hazy, barely functioning enough to keep the zombie upright. It can't properly remember its loved ones among the living, nor extend any empathy towards its fellow zombies.
How do I know this? The groans zombies emit do not seem to be any kind of predatorial behavior, nor a real attempt at communication. It is merely a reaction to pain and hunger. Also, while a zombie will do anything to satisfy its hunger, it doesn't seem to have any real survival drive