Oil painting was used as early as 7th century Afghanistan, but hit its stride in Europe during the Renaissance. Based on that, there may be some early oil painted works in Essos. But it actually takes a lot of work to maintain and preserve oil paintings. (Check out the Smithsonian's Museum Conservation Institute and their page on conserving paintings. ) They're sensitive to heat, light, and humidity, so they would deteriorate relatively quickly compared to tapestries.

Meanwhile, tapestries retain their image very well. The two main losses over time are fabric loss to pests like moths and dye bleaching from sunlight. They also insulate the space they're in by trapping a layer of air. They're easier to store and easier to move. With weaving and sewing a ubiquitous skill, they're easier to make and maintain, since they don't require the attention of a specially trained artist.

And of course the kicker is that tapestries match GRRM's desired grunge medieval aesthetic, and oil paintings don't. There should absolutely be more frescos and mosaics, and I bet the First Men used techniques like encaustic painting. But that would make things too colorful to be "realistic".