Mortimer Jones is Judy's father and one of Dexter's clients at the Sherry Island Golf Club when Dexter is working there as a caddy. Mortimer Jones is not a very dynamic character. Instead, he stands in for the wealth and privilege Dexter longs for.
Check out the scene, early on in "Winter Dreams," when Dexter is fantasizing about becoming a golf champion at the Sherry Island Club. He imagines himself playing in front of Mr. Mortimer Jones, who would watch Dexter "in open-mouthed wonder" (1.4). Clearly, making Mortimer Jones' jaw drop with his golfing talents would be proof to Dexter that he has successfully joined the upper classes.
Of course, that scene does nothing to round out Mortimer Jones for us. So if Mortimer is such a flat character, what's the point of including him in the story in the first place?
The fact that Mortimer Jones is Dexter's ideal rich man has two consequences for "Winter Dreams." First, his behavior at the beginning of the story foreshadows Dexter's disappointment with the rich life by the end. Jones begs Dexter not to quit his caddying job:
Mr. […] came up to Dexter with tears in his eyes and said that Dexter was the — best caddy in the club, and wouldn't he decide not to quit if Mr. Jones made it worth his while, because every other caddy in the club lost one ball a hole for him – regularly – . (1.5)
Check out how desperate Mortimer Jones is to keep Dexter working for him, since "every other caddy in the club lost one ball a hole for him — regularly —." If this guy is an example of the rich life Dexter is so eager to have, isn't it a little pathetic that he cares so much about losing golf balls?
What kind of life is this upper class existence, if it means you have to beg good caddies to stand by you with "tears in [your] eyes"? Golfing may be fun, but you shouldn't have to cry over it. There is a big difference between Mortimer Jones' silly worries about losing his golf balls and the kind of splendid dreams Dexter has about the glories of the rich life.
Second, Mortimer Jones' richness is what gives Judy Jones her easy attitude towards money and social class. Mortimer Jones is loaded, so Judy can frivolously spend her life seeking out pleasures and love affairs. It is Mortimer Jones' money that makes Judy the selfish, fascinating (to Dexter) woman that she is. Perhaps Dexter wants to be a self-made man so that his kids can be as careless and spoiled as Judy is.