It would lead to a far stronger Norse presence in the Americas, because the ultimate effect of any successful Vinland is to greatly strengthen the position of Greenland and to a lesser degree Iceland by giving them an easy source of timber and iron. Likely also trained warriors too, since there will be more clashes against the natives and likely others in the region, and that will be very helpful in repelling Inuit attacks in Greenland. Therefore, the Greenland settlements all remain and Iceland is slightly richer, meaning Norway or whichever nation has the Norwegian crown is far stronger entering the age where improved ships actually permit colonisation.
As for the natives, it depends just how big the colony is. There will be a formation of a mixed-race Metis population who will probably be the main conduit between Norse and indigenous culture. I think you'd see a syncretic cult based on Christianity in many native groups, although perhaps only practiced by a single society or clan grouping who may or may not have Norse ancestry. Given enough time, they might adopt herding sheep (the wool would be very useful), but I don't really see cattle or horses being too widespread. The latter two animals were too valuable to be readily traded and since American Indians are lactose intolerant, they wouldn't really be able to use dairy products (which the Norse preferred their cattle for). Horses are also pretty pointless in a forest, very rare in Greenland and Iceland, and even if a wealthy Indian bought a horse from a Norseman, he wouldn't know what to do with it besides slaughter it for food, which in Norse culture was considered a great offering.
Biggest impact is we'd see a native culture looking more like the 17th century Algonquian and Iroquoian cultures, which had changed greatly in the 16th century because of the introduction of European trade goods (mostly from Spain). They'd have slightly bigger, more organised populations and would almost certainly be using iron tools and clothed in colorful woolen robes (see old paintings of native chiefs for what I mean, these robes were made from cloth purchased from Europeans). These would likely be purchased from the Norse, but it's very plausible for a caste of Metis smiths to form. Likewise, I imagine they'd be using Norse-derived looms--weaving was a skill every Norse woman had, so if we imagine some Metis girls being raised by their Norse grandmothers or aunts instead of their "heathen" mothers, that's where the skill transfer would come from.
Their religion would be syncretic Christianity, which may either be widespread or limited to a single clan group of Norse-descended people. Some of this syncretic Christianity might be incredibly unorthodox, even by the standards of syncretic religion.
Now, the devil is in the details. It probably wouldn’t take long for horses to spread out and survive over, with the Great Plains looking a bit like the Steppes. As for the Appalachia, would still be used, but not as heavy. Horses would be the main beast of burden since I don’t think they’d be able to domestic muskox.
I think people underestimate the difficulty in teaching a radically different culture a skill like animal domestication. It generally took many years and far more direct contact than just a few trading missions. Even if we assume the colonies in Vinland and Markland are self-sustaining and grow to max population density (probably tens of thousands given the climate), that's still not a lot of people.
Metallurgy… most likely not. North America is pretty devoid of tin barring northern Mexico. If the vikings did explore the continent among the coast line and did make it Mesoamerica, then the idea of metal weapons there could be planted to see much greater usage of bronze weapons and leading to the development of iron weapons, especially if they discover the deposits in OTL Utah. As for Vinland, they could use the Iron deposits in Michigan, which would really enable them to become pretty powerful along with their native allies.
It's not, it's found in the southern Appalachians (Carolinas through northeastern Alabama), the same region where copper was historically mined by the Mississippians. Vinland wouldn't need the iron deposits in Michigan because there's ample bog iron in Newfoundland and Labrador. I suspect domestic metallurgy would spread to native cultures given enough time (at least 200 years, probably closer to 300-400 years), via the Metis population. Basic skills were widely known in Norse culture, so Metis individuals or even enterprising wanderers (who probably wouldn't show up before the colony is at its population limit) might know enough to kickstart local industry. It would certainly remain a closely guarded secret, limited to a particular clan group (IIRC this occurs among some African ethnic groups).
People are talking about Vinlanders bringing diseases with them and thus immunizing the native populations.
However, Greenland was very isolated from Europe; how much of these diseases were actually endemic in Greenland and thus would be brought over?
Greenland was pretty much epidemic free. IIRC the only suspected epidemic came from Iceland and may have been responsible for the decision to abandon the colony.
If anything came over, it would be minor diseases with long incubation times like mumps or whooping cough, both of which are very unlikely to be fatal but would cause a slight rise in infant mortality and likely famine because it would interrupt seasonal activities and sicken everyone at once. Chickenpox would also likely arrive via shingles, and that would be far more dangerous because it's very infectious and in adults can cause death. If you had hypothetical epidemics of all three diseases in the Americas, I estimate 5-10% of people would die from disease and famine. Chickenpox is interesting too in that it would almost certainly remain endemic because the virus can cause shingles later in life, and that can spread to the uninfected as chickenpox.
The effect would probably be beneficial in that it might give native cultures a sense of how to control infectious disease as well as what treatments work and what treatments don't against novel diseases. I bring that up because sweat baths were responsible for many deaths because they both spread disease and overheated people with high fevers which when jumping into cold water afterwards, would produce shock and almost certain death.