The last update on how he is treated:
https://www.computerweekly.com/news/252487666/US-decision-to...
I don't doubt that (almost) any other American taking shelter in Russia would make a dent on their reputation in US, but I'm curious about Snowden specifically. IMO, Those who know what he did and how he did (in general) seem to support him. A minority hates him. But the rest of public opinion?
I think the intelligence community and establishment democrats & republicans are generally still out to get Snowden, while his support comes from the fringes left and (libertarian-)right, who have basically no actual power.
Public opinion seems to be mixed and a lot of regular people don't have strongly held opinions about Snowden (or mass surveillance in general). The Patriot Act is still in effect for god’s sake even after all these revelations.
Lately the whole russia-gate thing has made it really easy to get people to froth at the mouth at any Russian connection, and the fact that Trump said he wanted to look at Snowden (Even a broken clock is right twice a day) automatically will turn anti-Trump people against it. So I don't see public opinion turning more positive on Snowden in the short term.
EDIT: I realized that my writing looks very GTP-3 like, but I swear i'm not a bot, I'm just having trouble connecting these thoughts in a nice way.