This phrase does not make much sense per se
Laiko -> means time's (or: of time, if you prefer, like the passage of time - laiko ėjimas), so:
laiko siaus pūga -> time's will-rage a-blizzard (which does not make any sense)
It would make more sense if it was 'už lango' ('behind the window'), which would make it 'a blizzard will range behind the window'. It could also be 'lauke' ('outside').
The other part makes more sense, except for 'širdį', which feels like it's used in the wrong case (accusative) instead of locative. Compare these two.
The current one:
The fixed one:
So, it if is slightly corrected, it would mean: a blizzard will rage behind the window, but there is still a cold winter in my heart. If not corrected, it would mean 'time's will rage a blizzard, and still cold winter my heart'. But it sounds like it was transcribed by someone who was either in a rush or was not extremely knowledgeable in the language and therefore it should be corrected.