Aaahhhh ... those wondrous nocturnal logs of wood! I don't necessarily like waking in the middle of the night, but when it's because my cock is raging hard ... well, now that's a whole different story.
Not counting the ones we purposely work up to enjoy, we get so many semi-boners and full-blown boners throughout a 24-hour period. They're BOE's (Blood Oxygen Erections). Most of the daytime ones, once we reach adulthood, are just semi's; we get used to them and can pretty much ignore them. A simple adjustment to the crotch and go on about our business. The morning boner will pretty much subside while we take our morning piss. Sometimes daytime boners can get demanding, twitching and throbbing and leaking pre-cum; those relentless ones we take to the men's room (or, more truthfully, anywhere we can find) and pound on until we relieve them.
It's the nighttime ones, when we're sleeping, that get the hardest. Though they get raging, rip-roaring hard, we're typically never aware of them. Maybe they cause us to enter a sexual dream state. Maybe they cause us to have a wet dream (though the end of puberty usually signals the end of those). This is because we are totally relaxed, our minds at peace, in REM sleep.
Last night, my cock woke me up around 4:30 - hard as a fuckin' piece of granite. I arranged it between my stomach and the mattress and just couldn't stop my hips from grinding. Just a few thrusts to really enjoy the sensation of it being so solid, so hard, so sensitive. And went back to sleep.
You don't necessarily have to cum to derive pleasure from your pecker. So, if you become aware of it - if it wakes you in the middle of the night - take a few seconds to appreciate it. I encourage you to enjoy every single hard-on your cock brings to you.
But, if you feel like taking it all the way, go ahead.