"on summer days" is correct and usable in written English.
You can use it anytime you want to refer to days that occur during summertime. For example: "I like to relax on summer days by the pool."
I took my father to the pond Dan and I would go to on summer days and nights when we'd smoke and drink from little miniature liquor bottles I would steal from my parents' liquor cabinet.
He outfitted them with Rollerblades, and got them onto their bicycles on summer days.
Gaffin's group found that the white portion of the Con Ed roof averaged 43 degrees cooler than black at noon on summer days.
A picnic area is not far from the first set of pools, but it does get crowded here on summer days.
I completely agree with HVR's Robert Yasinac when he suggests it as worth restoring simply so residents of the nursing home can sit out and watch the river on summer days.
Direct temperature measurements conducted during site visits showed that synthetic turf fields can get up to 60° hotter than grass, with surface temperatures reaching 160°F on summer days.
Wild brown and brook trout swim in the rivers and reservoirs that supply New York City with its drinking water, luring scores of fishermen on summer days like this one.
On summer days the scene at the outdoor pools sizzled.
"We used to go there sometimes on summer days," he said.
On summer days, this is served on the terrace, to the accompaniment of birdsong.
On summer days, it rang with the whine of motorcycles and the crack of gunfire.
