All praise is due to Allah. May Allah's peace and blessings be upon our prophet Muhammad, his family and all his companions.
Travelling to non-Muslim countries is permissible with three conditions:
The first condition: The person should have a level of faith which can protect him from desires.
The second condition: The person must have knowledge which protects him from doubts because these countries are filled with various types of doubts which may be in a written format which a person may read. Others could be in the situation prevailing there whereby a person may be tempted by the reality, development, advancement and organization, and so on which he sees there.
The third condition: There must be a real need for travelling to those countries, and needs differ according to different people. Therefore, there is no criteria applicable to everyone in this regard.
For example, a person may want to travel to those countries because of a better level of studies, easier understanding of the area that he wants to study in, even though these studies may be available in Muslim countries. The studies in foreign countries may allow him to be appointed to higher positions, and open for him more opportunities. These are real needs even though their level is not like those of a person who studies disciplines which are not available in Muslim countries. My view is that these needs make it permissible for a person to travel to non-Muslim countries.
Therefore, if you are travelling to a country where Muslims are a minority, and non-Muslims are a majority, I advise you to fear Allah, gain knowledge and strengthen your faith. Knowledge will guard you from doubts, and faith will guard you from desires. Therefore, if there is need, there is no problem in travelling to non-Muslim countries.
However, you should remember that you are in a morally bankrupt country, where the people are not restricted by the laws of the Sharee'ah because they are not Muslims.
Therefore, you should keep this in mind, and prepare for it. If a person prepares for a journey by taking along food and drink, then it is more pertinent for him to prepare with regards to things relating his heart, faith and religion. He needs additional care in this regard.
As for the issue of a woman's covering of her face; there is no difference in that regard between a Muslim country and a non-Muslim country in principle. However, if a woman's covering of her face causes affliction for her, her husband or her family, then in this case she will be permitted to uncover her face because the Sharee'ah is based on Allah's statement which states, " So fear Allah as much as you are able " [at-Taghabun: 16]. If a woman is able to cover her face, then it is compulsory for her to cover her face. However, if this causes harm, certain and not probable detriment, then a concession will be given to the woman in accordance to what is appropriate to her situation.
It is permissible for a woman to uncover her face if there is need for that. The jurists of different mathabs stated that there is no problem if a woman uncovers her face because of need.
As for a woman's studying in a mixed university it is better for her not to do so because she may be tempted by the free-mixing of genders. Moreover, some women go to those countries and learn without being involved in inter-mingling with the opposite gender.