Not sure Red Haven is OK for Z5 or more accurately Z4 in my area, but I've planted a Reliant on the Eastside of the house and have actually gotten some very nice peaches from it.
Sometimes it was the last tree in the garden or in the woods to lose its green color. Oak trees were dropping some leaves before the peach dropped anything.
I believe adequate soil moisture very deep into the root zone is the most important aspect of winter hardiness.
Good luck with your Red Haven. :)

If you have not pruned your peach tree yet, you can do it now. Pruning helps to maintain the health of the tree and increases productivity. I finally found the time to prune my peach trees in early December and I am expecting great results next year. All my peach trees are fine unprotected in my chilly zone 5 location.

I thought that peaches musntn't be pruned in winter because of some diseases...

Most plants are pruned during dormancy to prevent diseases. The diseases are not active during the winter so the wounds of pruning areable to heal before the disease organisms get a chance to enter the wound.
At least that is what I learned, years ago. :)

From what I have read and learned, pruning peach trees should be done in late winter/early spring to avoid damages to the trees when cold winter hits. During winter, pruning will reduce the trees'cold hardiness.

Not all fruit trees are alike. Apple trees can be pruned in the dead of winter. Peach trees are more vulnerable to cold weather. Also, you need to be sure your peache tree variety can tolerate cold weather in your zone.

The protection I do in late fall when leaves drop is to spray peach trees with copper to protect them against canker. I'll spray it again in early spring. Sometimes, leaves drop so late, I even pick off remaining leaves so I could spray in late fall when the temperature is still OK to spray.

Hi Dennis! I agree with mamuang. I would also include a fungicide called 'Monterey Fungi Fighter'. You can find it on line. Buying the most 'cold hardy' peaches is some of the best advice. 'Bacterial Canker' is always looming around many fruit trees, so the spray of Copper is really necessary. Where I live, it is very damp and foggy during the summer, but my peaches are always firm until mid September, when they become ripe. I have 'Elberta and Belle of Georgia'. Merry Christmas! Mrs. G

MrsG47 hi

I think pruning can be done in spring as it said earlier. I think pruning in winter is not good idea, maybe it is possible in warmer area say Florida or so but not here. Did you saw my message about long range weather forecast? When i said Rhode Island i meant you as you said earlier you haven't seen any long range weather forecast yet. I have read those 2 varieties Elberta and Belle of Georgia. Maybe those work for you. I think Elberta is later variety than Red Haven, in my mind right now. Didn't check it in internet at this moment.

Maplerbirch hi

You said you have Reliant. Do you mean Reliance? What you mean by soil moisture? I think it might good if there is moisture in soil, so peach root don't dry.

Plant_ hi

Not sure about disease, but in winter hardiness way is better to prune in spring i think.

Mamuang hi

I think prunning could be done in spring, as you said in cold weather.