Slightly below freezing is not going to cut it, unless you're going for a swim, first off.
Assuming you wait until it's much colder than that, cold enough to actually make it possible to die of hypothermia, it's still going to be harder than you think... and it's definitely not going to be pleasant. You will definitely suffer, and you will take a long time to die.
If you're seriously considering this, look up the five stages of hypothermia and its symptoms, and consider why almost all the literature talks about hypothermia from cold water, rather than cold air. Then, I would recommend going outside when it's slightly below freezing, wearing summer clothes. You won't be at risk of injury or death, but think about whether you really want to endure that (and worse) for several hours as you freeze to death. Also worth noting that if you try and fail in weather cold enough to kill you, you're going to get frostbite (painful and often permanent) and could lose toes, fingers and even parts of your arms and legs as your body restricts blood flow to your extremities.
I come from a city where it gets down to -40 most winters, and tried walking out into the cold to die a couple times... I never lasted more than 15 minutes. Cold hurts. Your skin gets tight and sensitive, you start shivering, your teeth chatter (bit my tongue pretty hard doing this, that sucked), if there's any wind or even a breeze, the air feels like a knife that's cutting into your bones. You get severe pain in your toes and fingers, and any exposed skin. Then, as you're dealing with the unpleasantness and pain of being very cold, parts of your body feel like they're on fire (as your blood vessels expand to rush warm blood to cold extremities). In my case, while I was shivering and cold and felt like my fingers and toes had been smashed by a hammer, had the sensation of cold knives stabbing into my bones from the wind, my cheeks and ears felt like they'd been set on fire. And then I'd start getting disoriented and hallucinating (not the fun kind of hallucinations, the terrifying, nightmarish, desperately sad kind), and next thing I know, I'd be somewhere inside, warming up.
Apparently, people who stick it out into the later stages have it even worse ("paradoxical undressing") when the the cold causes nerve damage.
So, yeah, I do not recommend. If you're hell-bent on doing it though, I'd recommend being unconscious during all the unpleasantness. (This was my "accidental" death plan, back when I was serious about dying in a way that didn't get ruled a suicide - guy with a "drinking problem" passes out drunk in a snowbank and dies trying to stumble home from the bar.)
Wait for a cold night, don't bring the jacket or boots (wear thin pants, a thin t-shirt and light shoes), and bring something with you you can use to go unconscious. A couple bottles of liquor and some benzodiazepines, for example. Get far enough out, drink and drug yourself unconscious, and wait. It's important to make sure you're not wearing anything warm enough to keep you alive when you get where you're going, and by not wearing anything warm on the trip out, you get a taste of what's to come. If you find that walking out to die in a t-shirt is too unpleasant to bear, you know that you don't want to go out this way while you can still turn back... rather than suffering horribly, only to end up saved with severe frostbite on your face and arms, missing 4 fingers and 8 toes.
