Fairly simple question, but a broad one: Did the Sami people of northern Scandinavia have any impact on Norse mythology? If so, how?
Yes, both as figures in historical and semi-legendary stories, and possibly through borrowings of mythological themes and ideas.
History and semi-legendary material
First, let's note the actual historical background, attested in Icelandic sagas: it seems that Norwegian kings had some kind of traditional right to gather tribute from the Sami, usually through some loyal man of his. This is described in e.g. Egil's Saga. This tribute seems to have been very substantial and important to the Norwegian kings.
Somewhat less historical is the traditional role assigned to individual Sami in Norse sagas: as sorcerers and wizards. The Sami seems to have been held to be a people with strong and fearsome magicians, and some of the semi-legendary material is about how foolish it is to cross them. They are generally not hostile, but, if provoked, they will retaliate. They can also be dangerous for other reasons.
The story in Ynglingasaga of Vanlandi is a good example: the Swedish king Vanlandi visited the Sami, and agreed with their chieftain Snow that he would return to marry Snow's daughter Drift within three years. When ten years had passed and he had not returned, Drift went to a magician to cast a spell on Vanlandi: either he would return to the Sami, or he would die. Vanlandi was seized with an urge to go back to Sápmi, but his friends persuaded him to stay at Uppsala. He soon withered and died.
Stories as this can be interpreted as small-scale reflections of the larger mythology, with the Norse serving as analogues of the gods and the Sami as Jotuns. See also the story of Snøfrid and Harald Fairhair in Heimskringla.
This is a slightly less straightforward topic, as there much more room for interpretation, but it is certain that Norse and Sami mythologies shares some features. Whether this is due to borrowing either way or separate developments from a common ancestor is impossible to say for sure, but the traditional argument seems to be to associate anything that is faintly shamanistic in the mythological to the Sami, and the rest is considered Norse (or perhaps, "Germanic").
In particular, Seidr is thought to be a Sami practice borrowed by the Norse. There is a hint of this in Lokasenna, where Loki accuses Odin of "drumming like the Völvas", and that this was unmanly; Sami Noaidi would go into a trance through drumming a special drum (c.f. also the story about the Völva in The Saga of Eric the Red).
The above is mainly based on Gro Steinsland, Fornnordisk religion, except for some examples from the sagas.
The goddess Skadi, who skiied and hunted with a bow, is often seen as modelled on the Sami, especially Sami women. Since the Sami were seen as "other", with a different lifestyle, language and religion, the giants and Sami were often creatively confused, as both lived in Utgard, the Out-lands.
Andejons mentioned Harolf fairhair and his Sami wife Snaefrid, and her father Svasi is described as a Sami and a jotun (giant), and another story about Harold tells how he helped a man named Dorfi, who is also described as a Sami and a giant. I have based my answer on a paper by Else Mundal, who also thinks that the marriage of Njord and Skadi could be read as a parable on Norse/Sami relations.