Sword of Four Seasons - Input wanted

I was browsing magical swords to possibly award a player’s Eldritch Knight Fighter (level 5). This is the player’s first DnD group, so far he’s proven to be quite creative in his gameplay and I wanted to provide him with some options. He plays a loxodon with a (rice) farmer background and I thought something with the seasons suited that. He doesn’t use offensive spells and limits himself to spells such as Shield, Longstrider, Blade Ward and True Strike.

What I’ve got so far:

The sword grants him Weather Sensor, a trait from the Druidcraft cantrip, which allows him to locally predict the weather for 24 hours.

The sword has 4 “modes”, one for each season, with different abilities. At first these are cantrips, but if he likes the sword enough maybe the sword grows up with him and provides leveled spells. I think that every long rest it shifts to the next season, though this might be annoying to keep track of.

Summer gives him Green-Flame Blade, Autumn gives him Chill Touch and Winter gives a modified Frost (melee attacks only?). For Spring I thought Thornwhip, which fits thematically but not so much visually. So maybe a healing spell, but unlike the others it’s not a cantrip. Guidance?

Lastly I’m wondering about is its balance. If I understand correctly, GFB is the weapon’s damage + the spells damage? Should I apply this same math to the other cantrips used?

You can always flavor the Thorn Whip to your satisfaction. It doesn't have to be a stereotypical thorny vine, but maybe it's a lash of pure natural glowing energy. In fact, let your player describe what it looks like. They'll have fun and be more engaged when you let them make those little decisions.

Giving a sword a few cantrips likely won't throw things off very much. It gives the player some more versatility and helps them out in an area they haven't really put many spells into. Hopefully, Chill Touch doesn't break your game :)