Icelanders may have a difficult time when visiting countries where mosquitos are common. Especially being susceptible to mosquito-born illnesses that they would normally not come into contact with in Iceland. There could be ways to immunize people before traveling to countries with mosquitos so that they don't suffer the effects of some illnesses.
Mosquitos are dirty little pests. They carry all sorts of disease, but are a part of the eco-system and therefore valuable. The fact that there aren't any in Iceland is great for those residents. When they encounter mosquitoes in other countries it doesn't really matter. The diseases that they carry are the type that no one builds immunity to, whether they are used to living in mosquito-ridden places or not. So it really doesn't hurt anything for the people of Iceland to encounter mosquitoes when visiting other countries any more than anyone else.
Icelanders are not at a disadvantage since their country does not have mosquitoes. People from countries with mosquitoes can still face devastating illnesses like malaria. Being around mosquitoes does not make people immune to the diseases that mosquitoes can carry. Therefore, Icelanders are not in any additional dangers since their country is not exposed to mosquitoes.
Most of the things that mosquitoes carry around are very dangerous. These are not things that people can build up an immunity for. It's not like chicken pox where you mostly only get it once in life. Icelanders have the same risks when they travel to other places as anyone else.