My son is 7 months old, and we have an infant car seat that detaches from the base for easy transport, that also docks into the stroller. We use the car seat to carry him from the car to just about anywhere (although he's starting to get big enough that we sometimes leave the car seat in the car now).
We've never covered him while he's been in the car seat, aside from using the attached hood to protect him from rain/snow.
However, I've seen a lot of parents carrying their infants in similar seats, but with a blanket draped over the top to completely hide their child from sight. At first I thought that it was for parents who were transporting their infants early (we were told to keep our son at home for the first 2-4 weeks after we got home from the hospital, to avoid early sickness), and who were concerned about their baby getting sick. However, it seems way too common for that, and we've seen this done with children 6 months and older. We see it at restaurants, at the pool, at the pediatricians, and even from parents dropping off their child at daycare. In fact, this seems to be so common that we seem to be in the tiny minority by not covering him.
Is there a specific reason to cover an infant like that when traveling?