“Between hay and grass” is said of the seasons, it being neither winter nor summer. It’s also said of a young person, not a boy (or a girl) and not yet a man (or a woman).
 
   
Old West Writer’s Guide
Between hay and grass ~ neither man nor boy, half-grown.
   
(Oxford English Dictionary)
1891 J. M. DIXON Dict. Idiomatic Eng. Phr. s.v., Between hay and grass, in an unformed state; hobble-de-hoy. F[amiliar]. An Americanism, said of youths between boyhood and manhood.
       
March 1840, The Cultivator, pg. 38:
Comparatively little can be done in the fields at this season of the year, but the good farmer will find March any thing but an idle month. He will find it perhaps the most critical month in the year for his cattle and sheep, and that additional care will be required as the season advances, termed by farmers between hay and grass.
 
Making of America
Title: Six months in Kansas.: By a lady.
Author:  Ropes, Hannah Anderson.
Publication Info: Boston,, New York,: J. P. Jewett & co.;, Sheldon, Blakeman & co., [etc., etc.], 1856.
Collection: Making of America Books
Pg. 186:
...some snow and frost about the earth, and a curious—between “hay and grass”—aspect of people, cattle, and equipages.
             
21 April 1859, Alton (IL) Weekly Courier, pg. 2, col. 4:
Cattle look somewhat gaunt, as is their wont in this between-hay-and-grass season, and wander weekly over the closely gnawed pastures that satisfy the lusts of the eye rather than the weaknesses of the flesh.
   
19 April 1860, Eau Claire (WI) Free Press, pg. 1, col. 5:
There is a time in summer that may be called “between hay and grass” in reference to what the farmer finds upon his table.
     
Wright American Fiction, 1851-1875
Morford, Henry, (1823-1881): Utterly Wrecked ([1866]) 1 match in 1 of 182 pages
CHAPTER IX.
ies with the later portions of a story that is as yet only in its beginning. / The young man, “between hay and grass,” as they country people say of anything in a transition state—between t  
 
24 June 1875, Cedar Rapids (Iowa) Times, pg. 1, col. 2:
The late spring had such a retarding effect upon vegetation that we find ourselves in the beginning of summer in that undesirable position expressed by the saying, “between hay and grass.”
   
4 November 1879, Marion (OH) Daily Star, pg. 2, col. 1:
“No, sis, you’re neither a little girl nor a woman; but just between hay and grass, as one may say.”