When a Soldier comes to you and tells you they are having trouble in their personal life, do you counsel and call it complaining?

Absolutely not, personal life can (and often does) affect work performance. As leaders we are hear to mentor and guide. Part of being a leader is knowing your Soldiers and getting them help when required. If they trust you enough to open up and tell you what is going on then be the leader they trust and get them help before things get worse.

I can understand possibly counseling if it is an ongoing issue and they have not taken your advise/directives, but initially, leaders need to sit down with Soldiers, discuss the issue, and come up with a solution.

On the inside I roll my eyes, and cuss out his father. In reality though, go someplace private, get as much detail as possible offer advice and try to figure out a course of action to correct whatever the problem may be. Also so long as they aren't breaking the law, and don't present a credible threat to themselves or others, it doesn't go beyond the two of us.

No way, and woe unto the NCO under me that does.
A Soldier coming to you is a sign of trust - it means that you are doing something right as a leader. Turning them away or worse, counseling them for having the audacity to bring a personal issue to you is not how a leader takes care of Soldiers.