The phrase "a small cottage on" is correct and usable in written English.
It can be used when describing the location or setting of a small cottage, often followed by a specific place or feature.
Example: "We spent our summer vacation in a small cottage on the edge of the forest."
Alternatives: "a tiny house by" or "a quaint cabin near".
At the end, brimming with pleasure at their time together, Brooke Astor offered her grandson the ownership of a small cottage on the grounds of an estate her son would one day inherit.
Their summer house was a small cottage on a lake.
In 1997, my wife and I purchased a small cottage on Bantam Lake in Litchfield.
An hour later, I was standing outside a small cottage on a leafy street.
Vacant lots on the water are desirable, and if an out-of-town buyer purchases a small cottage on a waterfront lot, the cottage is sometimes demolished.
SIDNEY AND ELISABETH GARVAIS had a lifetime of memories tied up in their second home, a small cottage on 4 ½ acres on Block Island, R.I.
Sir John Middleton Robert Hardyy), a cousin of the widowed Mrs. Dashwood, offers her a small cottage house on his estate, Barton Park in Devonshire.
Alexander McCall Smith One summer, over 20 years ago, my wife and I went to stay in a small cottage in France, on a farm in the Auvergne.
When my parents bought our house in the mid 80s there was a small cottage next to it on the property.
Dr. August Liliencrantz, an Oakland surgeon, built a small cottage, barn and vineyard on 1,000 acres he purchased from his friend Claus Spreckels, the sugar baron.
Until a couple of decades ago — maybe more — there was another building on our property, a small cottage where Pete stored his tools and where various things that had once been of use to us were put out of the way until some decision was made about what to do with them.
