GoT isn't meant to be any century. There are ****ing dragons, zombies, blood magic, super fire, faceless men, etc etc... and people are crying about time passing as if everything else is believable
"Oh wtf! we get to see Jon at Eastwatch NOW instead of waiting a week! HOW TERRIBLE!"
My point is that ASoIaF was inspired by medieval Europe, therefore the technological level of Westeros should be comparable (and has been for the entire show, particularly the first 3 to 4 seasons). There was an internal logic to the way things worked and how people interacted with society and the world. This false equivalency that because the show is high fantasy anything goes and screw rationality or logical writing is preposterous. Why is this unhelpful strawman constantly thrown around when discussing genre fiction.
A big part of the show's appeal was the unromantic and demythologized nature of the setting and treatment of its characters. It was no small task getting from a to b, and a journey of that distance likely would have some effect either on the characters themselves or the world around them due to their absence or the simple passage of time. The journey was usually more important than the destination, and unlike a simple plane ride would have consequences.
At the very least Cersei's hair should grow; if she is indeed pregnant it should be farther along; her mercenary army should arrive; Dany's 100,000 Dothraki and horses need food and a place to camp, etc. I don't need to actually see the months of uneventful travel take place, but lipservice should be paid to the length of time that passed. Surely plots like Arya/Littlefinger/Sansa would have played out by then. If the separate storylines are playing out at different times then they should either be clearer about it or tell the story better/find a different way to accomplish what they want.
All that said, I think the entire "steal a wight" plot is ridiculous in the first place and a waste of time. How do they intend to find one? Do they think it'll somehow be alone instead of with an army (an army which they constantly talk about); how will 10 men accomplish this; why no horses/wagons/hats/heavy gear or weapons; why did Jon have to go anyways (why risk the KitN) when the only wildling they took was Tormund (and maybe two others).
But more importantly, what makes them think they can convince Mad Cersei to join them in their fight against the White Walkers. She's crazy and power hungry, I can't see a rational argument working on her. And in the meantime she has no army, why doesn't Dany take her a dragon (or three) and take her out in a strategic strike on the Red Keep (with little collateral damage). Or simply lay siege against King's Landing (unopposed) and get the people to rise up and expel/kill her.
Or why couldn't Dany fly directly there with her dragons, see the army of the dead for herself and possibly kill the white walkers/night king while she's up there in one fell swoop?
I always figured GoT was 11-12th century.
You're right, I was just thinking of how ASoIaF was inspired by the War of the Roses which took place in the 15th century. Somehow I forgot they already had cannons and firearms then, which were introduced to Europe in the 13th century. So while some of the political shenanigans may come from a later period, the actual setting of Westoros is the 11-12 century, as you said (with dragons taking the place of cannons).
My original point is that there was no way Jon & Co. were able to make a journey of nearly 2000 miles with a 12th century sailing vessel in less than at least one to two months.
Now, whether or not the show has stuck to that period is another matter. I first noticed it when a wheelchair (which is a late 18th century invention) was introduced in season 5, but quite a few others things have made it through the cracks, especially in the last couple seasons. The showrunners clearly don't care about modern anachronisms rubbing up against the established period aesthetic. Just look at Cersei, Euron & Dany's new fashion sense, Dragonstone's throne room or all of the 21st century dialogue they keep including.