I haven't read all the responses, but I can see you have a variety. I just want to add, for all those who say "there's nothing you can or should do," that it frustrates me when moms aren't considerate of other families because THEIR comfort level with illness is high. For many people, getting sick is a way bigger deal than for the average person! Many mom's of young children are also pregnant, which puts them at higher risk for getting illnesses worse, and makes for a miserable pregnancy regardless. Some have other health concerns or compromised immune systems. When my daughter was a baby my husband had cancer, and I HAD to be very careful about what viruses we brought into our home, because his life literally depended on it. Just last week I spent 3 days in the hospital because someone had carelessly brought their kid to my daughter's nursery too soon after the stomach flu and I got it (I have a high-risk twin pregnancy, and the flu put me into pre-term labor). People who assume that getting sick is merely an "inconvenience" for everyone else are not considering that there are MANY people for whom a simple illness can be very threatening for various reasons. In my view, people should be more considerate in public for the sake of the more fragile, and should check in with moms they trade around with (I know many are fine with minor illnesses).
Since you only have one child, you CAN save yourself a lot of hassle by avoiding minor illnesses. And you should if you want to. I'm not a believer that a child who avoids a cold or virus here and there is somehow going to have a compromised immune system later. They're going to get plenty of things, whether you like it or not.
This is tough, because it's a friend you don't want to hurt. I think it's totally normal and common though to ask (even every time) whether anyone is sick at all. Moms have different thresholds for what's ok with them, and just say what yours is. You can be lighthearted about it, even apologetic about how "picky" you are, and joke about how since you only have one you have a chance of avoiding things if you're a little neurotic about it (whereas moms who have several kids or use daycare have really no chance).