you can say: "d'estate usiamo la griglia" or "in estate usiamo la griglia", both are correct and mean the same thing.
But you can only say "siamo in autunno" - "siamo in estate" - "siamo in inverno" - "siamo in primavera"
WRONG → "s̶i̶a̶m̶o̶ ̶d̶'̶a̶u̶t̶u̶n̶n̶o̶"̶ ̶-̶ ̶"̶s̶i̶a̶m̶o̶ ̶d̶'̶e̶s̶t̶a̶t̶e̶"̶ ̶-̶ ̶"̶s̶i̶a̶m̶o̶ ̶d̶'̶i̶n̶v̶e̶r̶n̶o̶"̶ ̶-̶ ̶"̶s̶i̶a̶m̶o̶ ̶d̶i̶ ̶p̶r̶i̶m̶a̶v̶e̶r̶a̶"̶
The correct use of prepositions is difficult to learn (in all languages)
About 50 years ago, in an English Language class we were told that language ultimately changes according to what people prefer to say (they don't look up a book on correct usage before opening their mouth)! That is how language changes through time. In "Emma", completed in a 1815, Jane Austen described her heroine as "handsome, clever and rich". Nowadays it would be something like "cute, smart and well-heeled".
D'estate means in the summer. Di is a weird one, it and it's derivatives can mean in, from, some, etc.
L'estate is the summer. So yous be saying the summer we use the grill, which doesn't make much sense.
Question for native speakers, would in l'estate usiamo or usiamo la griglia in L'estate make any sense?
Unfortunate really. It is simply not referred to as a gril in the U.K. "To grill" is, without exception, understood to mean grilling something indoors. If you said "We use the grill in summer", people would wonder why you never used it for the rest of the year, since things only get grilled in the kitchen, indoors.
"Barbecue" as a direct substitute for "Grill" should be permitted as a valid answer here for English speakers.
I am not a native speaker, yet I get some useful information from the Internet. First, d' is usually the contracted from of di except in certain phrases like d'ora in poi (from now on), so d'estate has to be di estate. Next, as for the meaning from, di is in a spatial sense while da is in a temporal sense, so di estate cannot mean from the summer as summer is no way a place. Therefore, d'estate has to mean in the summer, and from the summer would be da estate.