The members of the department have traveled widely and they recommend it strongly. Living in a foreign country can be one of the most important educational experiences you have at Smith, if that is not a contradiction.
There is no particular reason to study mathematics abroad (the way there are reasons to study Spanish, Biology, Anthropology, for example). In fact, the mathematical resources of the country you choose to visit may be slim or difficult to access. (This is just as likely in a developed country as in an underdeveloped one). This should not deter you. If you plan ahead (and start planning, if you can, at the start of your sophomore year) you can take enough courses so that you need to take few or no math credits from abroad.
In one sense, mathematics is acultural, that is, the mathematical objects we study are constant, independent of the society in which they are studied. In another sense, however, they are a part of the culture and time which produces them. Different societies find different parts of mathematics attractive: they teach it differently, and their attitudes toward it are different. Observing this and other aspects of a foreign culture can be as rewarding as mathematics itself. In any case, you will find the department very supportive of any well-conceived plan you and your adviser draw up. You should also consult with the study abroad adviser, Chris Golé.
Some information on opportunities for the junior year is kept in the Forum, third floor Burton.