OED gives “midsummer” as on or about the summer solstice, which many will tell you is the beginning of summer, not the middle.  I suppose it all depends on whether you count by light or by heat.  The date can be set by the moment of solstice, or you can opt for John the Baptist’s natal feast day, June 24th.  OED does not include the hyphen, just a space, so for our purposes I’m calling this a JRRT spelling.

• 06.030 at Old Took’s midsummer-eve parties,

“midsummer, n.” OED Online. Oxford University Press, June 2015. Web. 28 July 2015.