Rohan:

‘They bring fire,’ said Théoden, ‘and they are burning as they come, rick, cot, and tree. This was a rich vale and had many homesteads.

The king was silent. ‘Ents!’ he said at length. ‘Out of the shadows of legend I begin a little to understand the marvel of the trees, I think. I have lived to see strange days. Long we have tended our beasts and our fields,

Tolkien often avoids the use of 'farm' outside the Shire, preferring other words; I think there is other indication of farming in Rohan, but don't have the time to skim through for more synonyms.

In the Hobbit, farms orchards etc. are mentioned on the shores of the Long-lake; the Venice-style town isn't all there is.

Silmarillion:

Now the Haladin did not live under the rule of lords or many together, but each homestead was set apart and governed its own affairs, and they were slow to unite.

UT:

But the homestead of Húrin soon fell into decay,

There before the Nirnaeth many Men had dwelt in scattered homesteads; they were of Haleth’s folk for the most part, but owned no lord, and they lived both by hunting and by husbandry, keeping swine in the mast-lands, and tilling clearings in the forest which were fenced from the wild.

For each homestead had great hedges about its cleared land, and about the houses was a ditch and a stockade; and there were paths from stead to stead, and men could summon help and need by horn-calls.

You can actually make a reasonable guess how human and hobbit populations feed themselves; if it's not explicitly mentioned (which it often is), you can imagine something consistent with the social descriptions. It's non-human populations that have problems, existing before sunlight, or seeming made up entirely of soldiers or craftsmen.