I'm planning to apply to a few jobs abroad, however don't currently hold any visa to work there yet. I was told by a few friends that I shouldn't mention that I'm a foreigner until I got the chance for an interview with the company. Is this a good idea though?
No, it's best to be upfront so no one wastes their time. Most jobs advertised would not be for foreigners. The ones that are are usually very clear about it.
Your resume should make it clear where you're located anyway. There is no point trying to obscure your location. It's a big specialised effort to hire foreigners and companies do not go to that length without good reason. An application out of nowhere that turned out to be someone requiring visa and accommodation would not impress.
Depending on the jobs you are applying to do and the country you are seeking to work in, you may not be eligible to apply. For example, in the UK if my company wants to employ a non-EU worker then we must show the government that we tried to fill the vacancy with an EU worker first. If you are not eligible then any application is wasting your time and theirs. You may want to post a new question on expatriates.stackexchange with more details of your plans