Why is it winter in Laketown?

According to the Hobbit Timeline, you can see that they arrived on Esgaroth on 22/9 (22 Halimath).

Halimath is the 9th month of the Shire calendar; on the related wiki article you can see that that corresponds to our own late September. So, considering that Esgaroth is kinda north and near a mountain, it is not unlikely to have snows and ices during early autumn.

In the novel, we can work out that the events of the mountain and Lake Town happen at the end of autumn and beginning of winter. There are no descriptions, directly, of "snow on the ground" or "ice in the water", but indirectly Tolkien puts us in that frame.

As pointed out by Shevlaskovic, the events happen in what would be to us, September. September is a month where, depending on the latitude, weeks can be unbearably hot (it is so right now, where I live) or cold enough for ice and snow.

Hints can be given within Chapters 13 and 14 (IIRC):

When Bard fails in his attempt to get Thorin to give up some of the treasure hoard to Lake Town, the Thrush tries to talk to Bilbo and the Dwarves under the mountain, but none can understand him. The Thrush then flies off and gets Roac, son of Carc, who is an elder Raven. Thorin can speak with the raven, Roac.

Roac speaks to Thorin about Thorin's reticence to give up portions of the treasury. He points out that it may be impossible for Thorin and the 13 to survive the coming Winter and that Lake Town deserves their portion of the treasure, since it was they who helped slay Smaug and the town was destroyed by Smaug. They need to rebuild before Winter comes.

The actual phrasing in the book was "before winter sets" (I believe). Tolkien wouldn't have said that, if it were Spring, or even Summer. But now, combined with the calendar knowledge, we can safely assume that Winter is just around the corner, and that Peter Jackson was more correct than not in showing broken ice chunks in the river at Lake Town.