Is it easier to get funding for a master's degree in North America or in Europe?
In many European countries you won't be able to get a scholarship for a master's degree directly from a university. Also local students don't usually get that. The research funding is mostly aimed at PhD students, because master's degree students aren't expected to do research at the level these funds are targeting. Also, the general perception is that if you're a master's degree student, the university is providing a service to you, not vice versa, so why should they pay for that in addition?

Depending on national / local regulations, you may have to pay a tuition fee or not. If there is a tuition fee, there may be programs to waive or reduce these. There may be opportunities to work as a salaried student assistant at the university, but you'd first have to start a study program before even being considered for that.

What you're looking for are usually national funding organizations or foundations that support students coming from abroad to do a master's degree in that country. These are very rare and come with specific conditions. One such example is the King Abdullah Scholarship Programme of the German Academic Exchange Service.

For these countries, it'll be a waste of time writing to individual professors about scholarships for a master's degree. Instead it might be helpful to contact the offices for international exchange at your target universities to ask whether they know any scholarship programs for their place that apply to you. Or maybe you have such an office at your home university that has a list of programs for their students who are interested in international exchange.