But "has frozen" in English is the present perfect. The tense is present and the aspect is perfect, which means that the temporal point of reference is the present moment (the tense) but the event is already complete at that point of reference (the aspect). For the phrase to be in the past tense in English, while still being perfect in aspect, it would have to be "had frozen," referring to an event in the past which at that point was already complete. Other aspects in English are the progressive (is freezing, was freezing) and the simple (freezes, froze). It is also possible to combine the perfect aspect with the progressive aspect (has been freezing, had been freezing).
This is not to imply that on jäässä is at all a present perfect construction in Finnish. Technically, jäässä is the inessive singular of jää, "ice," so jäässä literally means "in ice." There seems to be a handful of expressions in Finnish of the form olla + inessive indicating that something is covered in something. In this case, the river is covered in ice, so to speak. Translating this to idiomatic English is another reminder that different languages work in fascinatingly different ways.
This is not "has" frozen its "is frozen" jäätynyt would be has frozen
Literally "is frozen" is "on jäätynyt" (time format perfect) but in Finnish is same as "on jäässä".
järvi jäätyy -> the lake freezes (present)
järvi jäätyi -> lake froze (imperfect)
järvi on jäätynyt / on jäässä -> the lake is frozen (perfect)
järvi oli jäätynyt / oli jäässä -> the lake was frozen (plusquamperfect)
järvi tulee jäätymään / tulee olemaan jäässä -> the lake will freeze (future)
I am freezing -> Minä palelen / minulla on kylmä / minä jäädyn
It's cold here -> Täällä on kylmä / tänne jäätyy (täällä jäätyy)