I agree with Carang. Colds are caused by a virus and have nothing to do with how many clothes you have on. Too few clothes might cause hypothermia, not the common cold. The reason we catch more colds in winter is because we are inside more, not because it is cold. Personally, I think you should allow your helper to wear whatever clothes she is comfortable in. Parents in HK seem to overdress their children, winter and summer (no offence to anyone, just a general observation).
It sounds like you want to keep your helper, but require her to improve her performance. Would you consider either a performance review - noting what she does well and not so well? If you really feel strongly, perhaps a formal warning letter. I have to say I don't like people coughing around my baby and I don't think you are being unreasonable by asking her to stay away from the baby or by wearing a mask. I know it builds up immunity, but no mum likes a sick child.
If your helper is new to HK, she is probably being exposed to new viruses that she hasn't had to fight before. When I first came to HK I had a couple of bad winters and now I hardly catch anything. Perhaps ensure that her diet is adequate - fruit and vege in particular and consider a multi vitamin. Does she get enough excercise - eg. a walk in the sun and fresh air each day. Does she get enough rest and sleep. Sleep is sooo restorative for the body and most adults need 8+ hours a night (although we don't always get it). Having some time to herself is also good for overall health. Can she have a proper lunchbreak during the day? What time does she finish working for you at night? If it is late, can you cook and clean up from dinner at least a couple of times a week to give her a break from working all day?
Anyway, just a few suggestions, feel free to disregard anything that doesn't work for you.
