The ga1-3 mutants do not respond to vernalization in short days...

Koorneef and van der Veen (1980) and Wilson et al. (1992) were the first to notice that ga1-3 mutants are insensitive to vernalization in short days, and concluded that there was some connection between the two pathways. However, this hypothesis vas invalidated (Michaels and Amasino, 1999; Chandler et al., 2000).

... But their ability to respond to vernalization is not affected:

In long days, the ga1-3 mutants expressing both FRI and FLC functional alleles, as well as ga1-3 mutants expressing FCA, do respond to vernalization (Wilson et al., 1992).

Michaels and Amasino (1999) analyzed the possible interactions between these 2 pathways, observing flowering time in three different photoperiods:

In 8h days (short days), vernalization accelerates flowering in the WT, but does not make ga1-3 mutants able to flower.

In 10h days, the WT flowering time is very similar to what it is in short days, with or without vernalization. However, the ga1-3 mutants do indeed respond to vernalization: they flower when they are vernalized, whereas they still do not flower if they are not vernalized.

In 16h days (long days), both the WT and ga1-3 respond to vernalization, which accelerates flowering by a similar number of days in both genotypes.

To further investigate the response to vernalization, the authors studied the flowering time in La-er ecotypes introgressed with functional alleles of FRI and FLC (These plants were therefore fully sensitive to vernalization). They found that, in both WT and ga1-3 backgrounds, there is a strong response to vernalization. Therefore, the ga1-3 mutation does not alter the ability to respond to vernalization.

GA1 and FCA promote flowering through independent pathways:

The possible connection between the GA and vernalization pathways was also investigated by Chandler et al. (2000). However, these experiments were done in 10h-long days, in which the ga1-3 mutants do flower, albeit very late. In these experiments, ga1-3 is late-flowering and not affected by vernalization. However, the WT is not much affected either. The fca-1 mutant responds strongly to vernalization, and the double mutant fca-1 ga1-3 also responds to vernalization and flowers at the same time as the ga1-3 single mutant. This means that, when ga1-3 is in a vernalization-sensitive background (such as fca-1), it does respond strongly to vernalization. The conclusion is that the GA pathway does not interact with the vernalization pathway.