my dd is also almost 3. Up until this year she has been very resistant to colds: sometimes we would have someone from abroad stay over and their child gets sick like the day before, so I could not tell them not to come since they had nowhere to go, and she would not catch anything even after being with a sick child in the same room.
But this year something has changed: I cannot even count how many colds she has had and she does not go to kindergarten. I give her probiotics and stick to the same hygiene measures as before but she seems to catch every bug around: and she only sees 1 smaller child on a daily basis.
So go figure.
Here in France kids go to "school" at 3, so if I keep her at home, she will by no means have a normal childhood, I guess you are lucky in the US to be able to keep your child away from kindergarten without it becoming a bubble for him.