Will 2 year old be okay for a quick walk in very cold weather?
Should be fine - I'd put a scarf over his mouth so it slightly warms the air before he breathes it in.
Of course it'll be okay. I raised 7 kids and it was a fight to keep them out of the cold.
Soooo obviously it doesn't matter does it.
He will be fine as long as he is wrapped up well
In some parts of the world the climate is extremely cold for months on end, and yet the children survive and thrive outdoors for quite a few of their waking hours. Just wrap him up and he will be fine. I assume that is 10 degrees Fahrenheit - 10 degrees Celsius (Centigrade) is a fairly mild spring day.
If you bundle him up really well he will be fine. Layer his clothes, make sure he has on thick mittens and a thick hat that goes well down over his head and ears. There is nothing wrong with taking a tot outside in the winter.
10 degrees? He'd be fine at -5 if you wrapped him up. Children play in snow, and it's a lot colder than 10 degrees then!
Just bundle him up really well, taking care to cover as much skin as possible. And do the same for yourself. If you take a stroller, add a blanket. Your walk will take less time, but he'll also get cold sooner if he's sitting still instead of walking. I would take my child walking as long as there isn't a strong wind. Otherwise I would take a taxi. Wind chill factor is a real thing.
make sure he is dressed warmly
What kind of clothing will he be wearing? He needs to have a full snow suit and parka, with hat, gloves, and boots. You will also need to carry him if he is wearing the appropriate warm clothing because it will slow him down significantly. He should be fine, but it will probably take you longer than you think because kids make everything seem to take longer.