The Rohirrim were much more Ango-Saxon, early English, than Norse. Some think it was a fancy of Tolkiens to take the saxons of old and make them extraordinary horsemen, as it was their lack of cavalry that saw them lose to the Normans at Hastings.
As for Norse, there is a fair bit of a mix in ME. As the previous poster said, Dale men, Rohirrim and a few others are Northmen, so Dale has more of a eastern feel but with, if the Hobbit films are to be believed, Nordic housing structures along with their naming. (Bard and Brand are both Nordic names)
The Rohirrim are obviously Saxon, as I said and therefore related to Norse stock, flowing pale hair and swirling patterns, longhalls and a rich spoken word record of their heritage.
The Dwarves have the most Nordic names. In fact many of the names of Thorin's company come from the Eddas. The magic behind their metal work is a very Norse trait, as well as some of their virtues. Then there is obviously the axes
I'm actually RP'ing a Variag now. Although a few, Games Workshop to name one, has painted these figures as a cross between Mongols and Samurai I'd strongly disagree. Nor do I agree with lotr wiki saying they are Hunnic. Tolkien only talks of them at Pellinor Fields by referring to them as "Fierce, bearded men wielding axes." They are allied to the men of the east, but different from them. All of this points to me towards the Varangian Guard, whom through the Sagas Tolkien would have been very familiar with. They were norsemen who went to seek employ with the Emperor of Constantinople, becoming his most trusted bodyguards. They were referred to in some tales, (as well as a Turisas song ) as "Axe wielding foreigners."
Through this I can only picture a group of Northmen who in the early third age went east, swearing their service to the Chieftains and Kings of the Easterlings in return for glory and gold. At least that's how I play mine
So long story short a typical Norseman might be hard to do, but if you can pick what traits attract you most to that type of character, you have plenty to choose from.
I hope some of this helps