As u/jacobhamselv noted, they certainly knew about Denmark, and sometimes faces raiders from there. Apart from the (debated) origin of the Teutones and Cimbri, the peninsula of Jutland isn't that far from the Rhine, the border of the Empire; and Roman armies occasionally penetrated as far as the Elbe, which flows into the North Sea at the base of Jutland. Moreover, Roman goods and coins have been found in Jutland, which suggests that traders at least knew of its location. Finally, the Romans had a navy in the North Sea, even if it stayed near the coast, so for them not to know about Jutland would be inconceivable. Cf. Tacitus Annals 2.23-24.

But they also certainly knew something about Scandinavia. They didn't know how big it is, and in fact they thought it was an island -- not unreasonably, because it's only connected to the continent far, far in the north-east, well beyond the boundaries of Roman geography. Tacitus Germania 1 refers to huge islands in the ocean bordering continental Germany, which is taken by most commentators to mean Scandinavia (e.g. Much, Die Germania des Tacitus, p. 10, in German). Pliny also seems to refer to Scandinavia as an island; compare 2.246 and 4.96. He also suggests, correctly, that it's much bigger than the portion they knew about, but that information was hard to come by. (Europe was much colder in antiquity than today, so ancient Scandinavia must have been *freezing*.)

Pliny (2.167) and Velleius (2.106) both mention a naval expedition under Tiberius that explored the northern ocean, but it's not entirely clear to me if they only went to Jutland or in fact Scandinavia proper.

Much's commentary on the Germania collects a lot more evidence, which cumulatively makes it clear that the Romans definitely had good information about continental Denmark, and probably knew a decent amount about Scandinavia, although they thought it was an island.

Edit: The temperature of ancient Europe is controversial. u/RiddleOfTheBrook and u/couplingrhino cite several modern studies suggesting that it wasn't very different from today, and the latter also suggests some reasons why the Romans described Europe north of the Alps as being so cold (they're Italians). They are probably correct. On the other hand, literary sources from antiquity describe things that can only be true if the climate was in fact significantly colder. Julius Caesar, for instance, reports finding reindeer in France. The Rhine is also reported to have frozen solid several times between 350 and 450, which is a much more rare event in modern times. I'm a philologist by training, so I tend to (over?)value contemporary written sources.