how cold can a chicken stand??

No, it is not too cold.  As long as they can keep dry, you are fine.  I'm in Indiana, and my girls would think they were in heaven if that was all the colder it got.

Welcome to BYC.  I live in Lucerne Valley, Ca.  That is the high desert area.  Our winters can be cold...30's.  I do not have a barn.  My birds are in coupes outside.  I put OSB boards around the coupes at this time, the coupes are wooden frame and wire.  They have a roof of OSB.  They are protected from the rain, for the most part, but when it is cold, it is cold.  Yes, I loose a couple of birds in winter.  Most of them do quite well.

You see, they also have extreme heat in the summer as it can get to 115 here, but it is not a humid heat so the shade takes care of the problems.

My coupes are pictured on my member page, which is found under my screen name.

I do move my birds around.  They adapt.  I have noticed however, sometimes a bird will be raised with another bird and choose it as its buddy.  They do better staying together.  When one dies, the other bird will miss its buddy.  Yes, they have personalities and you will learn that soon.

Best of luck to you, it is a big chicken world and it is hard to limit yourself...you will see.

Ok, the rain issue.

Best to keep them dry.  A young bird will huddle when frightened and could actually kill another bird.  They can drown in the rain as well.  Since my coupes keep out most of the water, I do ok.  I just put down dry straw on the floor.

Ok, I just heard you say something...chicky.  Are these three chicks living in a plastic tote?

Chicks need heat.  Grown birds are a totally different issue.  Look at the learing center area about raising chicks.

Chicks need heat...heat lamp...enclosed area...mother hens warm body.
Chicks can not retain their body heat and will die if cold.

And, in a "Plastic" tote, there is poor air circulation...not a good thing.

Dry dry dry dry. Its important that the your chickys can get to a dry area if they want to. Mine play in the rain on occasion but they can get dry whenever they want. Their coupe is 30 inches off of the ground.

Welcome to BYC, and to the world of raising chickens.  When they have all their feathers, and are big enough, they can stand rain just fine, mine toodle around in awful weather all the time.  I live where it freezes and snows regularly as do many others here, and chickens are happy in all kinds of climates as long as they have a dry place to shelter at night.

I'm sure you've looked at all kinds of pictures here of chickens walking around in snow and everything.  Yours will be fine if they have a sheltered place to go into for the night and lots of clean water and healthy feed.

It isn't really clear how old yours are, but once they have all their adult feathers, they can handle most anything your area will throw at them weather-wise.  Weather in the 50's will be no challenge for them.  Move their house around all you want, you say your yard is on the small side, so that wouldn't bother them.  (large distances -might- confuse them, but I'm talking a quarter mile or more! your yard will be fine!)