According to mobygames, these golf games were released on both the Atari ST and PC (among other platforms):
Arnold Palmer Tournament Golf
David Leadbetter's Greens
Greg Norman's Shark Attack! The Ultimate Golf Simulator
Hole-In-One Miniature Golf
Jack Nicklaus' Greatest 18 Holes of Major Championship Golf
Mean 18
Sporting Triangles
Will Harvey's Zany Golf
World Class Leader Board
However, most of these games are pretty old so I doubt they had any online multiplayer.
As for the online service, I didn't really play much multiplayer during the mid to late 90s but I did read about them in magazines and such, ogled at the logos etc. Even though I never really used services like
Ten.net,
Heat.net,
Engage Games Online,
Mplayer.com or
Kali, there's just something about 90s multiplayer that gives me all of the nostalgic feels, alongside all of the edgy commercials and cool demo discs. Anyway, it could be one of those services, but there were probably more.
Heat.net always reminds of some advertisement pages in Computer Gaming World (I still have the issue and the demo disc, #156) about Blood.