Some of the other answers have made headway, as regards the definition of 'mine's a G&T', but the entire point of the quote is really to define this couple in a single sentence.
They are both middle-class, from a time when that was 'more important' to be recognised as such than it is today.
He has gloves which suggest he drove a sports car or Jaguar*, which would define his drink as G&T rather than beer. Her mode of dress would be appropriate to that & a weekend at the horse trials.
It defines an entire class & culture from (probably) the 50s/60s in one sentence.
Below is a comment on the outmoded class-structure in the UK at the time, not my personal opinion...
*This would make him one of the class defined by those not belonging to it as 'The Gin & Jag Brigade'. It was a derogatory description, usually used by those who would prefer beer, even if they could afford the car.
'Horsey' describes the type of person who would attend gymkhanas & horse trials & describes the kind of attire one would wear to those... but (if it were not the author talking about her own mother, but a general perception of those times) could be a double 'attack/criticism' on not only the social class of the woman, but also her (alluded to) visual appearance. Large-framed, broad-hipped, long-faced; similar appearance to the horse she is accustomed to riding, or did in her youth.
Note that even in these times, the description 'horsey' wouldn't ordinarily be applied to someone with merely the physical appearance mentioned above - it would have to go hand-in-hand with the social definition.
Refs for 'the Gin & Jag Brigade'.
I can't find a dictionary definition as yet, but a couple of newspaper reports using it in such a way that it's obvious they fully expect their readership to already be well-aware of the term.
The Telegraph - They can't mean us
The Guardian - Town bristles at 'gin and Jag' slur
Urban Dictionary has a non-authoritive definition
Also... Ask Andy About Clothes but please take your social-responsibility-for-the-easily-offended hard-hat with you to this one, which is full of 'colourful' explanations - though technically just about SFW (safe for work).