| Anyway, the paint is starting to peel and chip from the cold and snow.
| Should I paint it again and if so with what kind of paint?
|

It's up to you. If you paint it you'll need to scrape
the loose paint and then it's a good idea to wash it
with a weak solution of TSP in hot water. (Maybe
1 tsp to a alf gallon.) For the paint I would use water
base "stain". Unlike most paints, it doesn't produce a
film, so it doesn't peel. It just wears off. But despite being
called stain it is an opaque paint.
It's easy to slap on another coat with stain, and
eventually you'll have no paint left to peel as the
old paint gradually comes off. One can even add water
to the stain to create a sort of primer, or soak the wall
first to make the stain soak in, but that shouldn't
be necessary.

I really like Pratt and Lambert stain, but lately I
can't get P&L. I don't know if it's being discontinued,
but the dealers near me have discontinued it.
Sherwin Williams owns P&L and their paint is pretty
good, though I haven't tried their exterior acrylic/latex
stain. Benjamin Moore is popular in my area, but their
products have been getting downgraded and often
changed in recent years. I'm not wild about their
water-base exterior stain. But any of those options
should be better than getting a Home Depot product.

If you use an enamel (a paint with a film) it tends
to peel because moisture migrates through the concrete.
For the same reason, concrete outside should never be
painted with oil paint. Likewise with asbestos or concrete
siding. They need to breathe.