Are the piles even, or in any particular shape? I ask because I’ve seen old wood cabins that were raised off the ground to prevent rot and they used dry stack stone pilings for the foundation. 150+ years might have rotted all evidence of any structure away and left the piles of stones.
Hold on there, I live in Southeastern Connecticut and I could take you to at least half dozen old homestead foundations built entirely of stone…rough cut field stone dating to early 18th century. Many of the out buildings and areas have rock mounds like the one in the OP. They are not cairnes. They are drawn and plotted field stone, or middens. Middens had stone placed over them to cover the stench…probably didn’t work very well, but early homsteaders did it anyway. It also kept animals from diggin in there.
Wood is still cheap in Noth America and it had the dual advantages of being easy to put up with labor that did not have to go through a lengthy apprentice program as well as actually being considered a nuisance. Any acre that was wooded was an acre that could not be planted. Even if you wanted to keep a few odd woodlots on your property for their scenic beauty (or, more likely, for firewood, game, or syrup, or something), your neighbors still had lots of woods preventing them from getting another acre of corn, tobacco, cotton, or wheat planted, so there was always a ready supply of lumber.
THINK, man! You’re in New England! The only crop you raise is stone, 
We see the same trend in NE Ohio. Most of the land was logged off for frame houses, but there are a couple of areas where the glacial moraines that form the backbone of the country pop up with enormous mounds of fragmented stone. There are also a couple of places where the early settlers found good quarry stone. In the villages near either of those occurrences, there are quite a number of either field stone houses or dressed stone houses (depending on the deposit near which the house stands).
I am surprised there aren’t any stone houses in your neck of the woods. Where I am from, Loudoun County Virginia, and the surrounding environs, there are tons of old stone houses dating back to the 1700s and 1800s. They are so beautiful. Here are some examples:
The famous Stone House at Manassas National Battlefield Park
Gorgeous old stone house for sale in Shepherdstown WV
Oakland Green Bed and Breakfast in Lincoln, Loudoun County, Virginia
Georges Mill Farm Bed and Breakfast, Lovettsville, Virginia
Various old houses in Hillsboro, VA
Article about Hillsboro, Virginia,‘Town Made of Stone’
(Ok let me wipe up the pool of drool from looking at those gorgeous houses…)
I vote for the field clearing rock piles also. You find them all over in the woods that have regrown. Indian graves were mostly dirt mounds or raised wood pallets on poles. and caves being sometimes used in the arid states, but this of course is a generalization with exceptions. You never know for sure without research. An older resident of the area may remember the place being a farmers field, and it was his daddies farm.
We still have many beautiful stone houses in the Caledonia Bluffs between Portage and Baraboo.
I’ve seen many such cairns in the woods of north Georgia, too. I’m also inclined to believe it was where land was cleared for cultivation.
(Halloween’s over, but here’s one more zombie: )
I’m resurrecting this thread because I found some new information. While researching an article I came across this paper on stone mounds constructed by Southern Indians (pdf file). It includes lengthy discussion of clusters of small mounds of the type you describe.
Ah, thanks. I look forward to reading that.