4x4typ says that GPS usage by non-residents is prohibited in Russia.

Some changes to the legislation took place, making it more loyal to GPS usage, but they relate only Russian residents. There might be some alterations for foreigners as well, but it is most likely that the prohibition is set up only indirectly now.

In any case, the foreigner walking with GPS is at risk of being involved in problems with aythorities, especially if he is watched by state security people or is near secret objects and territories.