Siberia is huge and largely empty of humans, giving plenty of space for tigers to hunt and their thick coats help them resist the cold.

Were there tigers in Scandinavia in historical times? It was still pretty empty in Roman times for instance.

Nope tigers were never present in either Europe or Africa.

Why?

The Siberian tiger lives almost exactly half way around the world from Scandinavia. It lives on the eastern coast of Siberia while Scandinavia is to the west of Russia. There were other tigers living closer, the Caspian tiger. But this have recently gone extinct due to the vast amount of forests that was converted to farmland in the 19th and 20th century.

Tigers generally prefer large sparse forests and have adopted to these conditions. Scandinavia have a lot of dense forests and mountains which is not the type of area the tiger prefers. So if tigers did at some point push more into Scandinavia, for example from Ukraine, then they would have been out performed by wolves and bears who are much better in those kinds of conditions.

They evolved in Asia and would need to cross terrain that isn't good for tigers to hunt in.

Was there ever a tiger-like large cat in Northern Europe? (Not limited to Scandinavia)

There were prehistoric lion species in north/central Europe during the ice age, as far north as the UK.

Scandinavia was largely covered in glaciers at the time so I don’t think their range extended that far north.

There were lions in Europe.

How far north did their range extend?

Not really. The has been a lion in Greece and the Balkans up to Hungary and Ukraine. The last one survives in part of Greece until 4th century AD.

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Northern Europe has quite recently been covered with ice and human migration has followed the retreat of the ice. The large ice cover had its largest extent 20 000 years ago when it ended in northern Germany.

The lynx is the largest feline, wolf, and bears are the largest predators.

Exactly what life was there before the last ice age is unknown. A kilometer-thick layer of ice even smooths out the bedrock so there is no evidence of what lived in Scandinavia before the ice retreated. That is lived recently before it, there is evidence od what lived millions of a year ago in for example sandstone formations.

In human civilisations Greece was about as far north as they got further north and the wolves and bears were far better suited to the conditions.

Siberian tigers only technically live in Siberia

Sibera is all of Russia west of the Ural mountains which is like 80% of Russia's area and like 4000 miles wide

The Siberian Tiger's range is Korea and the edges of China and Russia near there. Technically that part of Russia is Siberia but Scandinavia is closer to New England than the tigers range in Russia

Yeah, there used to be lions and leopards all over Europe during the ice ages. They may not have been that far north, though, because there were glaciers covering that far.

We used to have jaguars in Canada overhead in N.America.

A long time ago, there were some species of saber-toothed cats. Today there's the lynx, much smaller, and, just at the edge to Asia, a leopard subspecies.

The part of Siberia where the tigers live isn't the stereotypical taiga you are probably imagining. Google "Ussuri broadleaf and mixed forests", "Sikhote-Alin Nature Reserve" or "Ussurisky Nature Reserve". It's very far south, far enough that the boreal taiga is replaced by a temperate forest, not unlike those in China, Korea or Japan.

Amur Tigers (the largest species) survive just fine in Kamchatka, despite it's sometimes mountainous terrain. While they do prefer less hilly terrain, they manage just fine within it. The lack of human population is more important for their survival, hence why they have been pushed out of northern China.

Still have Cougars . . . and not just in Toronto dance Clubs.

And, technically, the "Siberian" Tiger is actually called the Amur Tiger.