During the baseball off-season, many players and fans undergo a variety of workout regimens designed to keep the body in shape prior to the rigors of Spring, Summer and Fall ball.
With snow on the ground and temperatures not conducive to most outdoors activities, heading down to the the Southern states is probably the best way to avoid winter blues and get some low-stress exercise while enjoying a warmer climate.
There's a contention that swinging a golf club will damage one's baseball swing, but there's no scientific evidence to back up the claim, and, in fact, hitting a stationary golf ball off a tee is the perfect alternative to keep hand-eye coordination at a maximum level.
For the sheer enjoyment of the game (why not have some fun while staying in shape?) try some premium golf balls that will play better than what most of us usually use, and maybe, for the home-run hitter in all of us, pick up some specialty distance golf balls and get some real bang out of that driver.
There's no need to be concerned about your baseball swing. A few rounds - or even a couple dozen - isn't going to affect your plate approach, any more than playing squash or racquetball in the off-season would impair a tennis swing.
Be sure not to go by cart unless it's mandated by the course. Walking 18 holes is good low-impact exercise in its own right and the contemplative nature of wandering down a lush fairway is also good for clearing the mind.