Hello fenix.io
Thats strange - originally saves from 0.3 are work fine with 0.4 and there no need to transfer anything if you are playing on same pc, new version will automatically get your previous save files.
If you have any problems with save files please DM me on Discord we will fix it. https://discord.com/invite/6JF9HEN
P.S. As workaround you can try to load sometime before 0.3 ends (Country house event as example).