Rangers have the spellcasting class feature. It allows the Ranger to cast a small number of spells from the Ranger spell list, which has a lot in common with the Druid spell list (much like the Paladin spell list has a lot in common with the Cleric spell list, although they aren't the same; Hunter's Mark for Rangers and the various Smite spells and Aura spells that Paladins get are examples of why they aren't literally just subsets of the Druid and Cleric spell lists).
The "Druid-y" feel of the Ranger spell list suits the more "nature-y" feel of the standard Ranger, such as those with the Hunter or Beastmaster archetypes from the PHB. But what about the archetypes from Xanathar's Guide to Everything? To my mind, they seem less "nature-y", and thus the "druid-y" spells they get don't seem to suit them as well. To clarify, it's not the "free" domain spells you get as per each of the archetypes from Xanathar's, but rather than default Ranger spell list, that I feel doesn't suit a less nature-y Ranger.
The character I have in mind is a Horizon Walker Ranger who is interested in threats from other planes, which to me says that such a character would be more interested in the Arcane than in nature and "Druid-y" spells. Why would such a Ranger who studies portals and other planes be able to cast Plant Growth, for example?
I plan to ask my DM (if and when I make this character; they're a "backup" character idea at the moment should my current character die) if I could essentially choose from the Wizard spell list instead of the Ranger spell list, but otherwise have the same restrictions as per the Ranger table in the PHB (i.e. no cantrips, same number and level of spells, the same number and level of spells slots, can't use an arcane focus, etc). I would also leave the domain spells that you get for "free" as per the Horizon Walker archetype as-is.
Since I'll be learning Wizard spells, it might also make more sense to use INT as my spellcasting stat rather than WIS, but I've asked about that in a separate question (hence for this question, just assume I'm still using WIS).
My question is: What are the impacts of a Ranger using the Wizard spell list? How will the Ranger having access to, say, fireball affect balance? If this is overpowered, would restricting access to certain schools (a la Eldritch Knights and Arcane Tricksters) help to rebalance things?
I am considering multiclassing into Wizard, but decided that I didn't really want to do that. The DM isn't too keen on multiclassing, at least not in this game as, although he's a long time player, it's his first time DMing and he doesn't want to deal with multiclassing. This is why I want to have some backup to convince him of this idea of mine. He's already let someone play the UA "Revised Ranger", so it seems to be just multiclassing he doesn't like.
It isn't my intention to make my Ranger overpowered, or even any more powerful than the default Ranger. My core problem is that I don't think "nature-y" spells suit him, whereas arcane spells would suit him being interested in extraplanar threats. In particular, I personally was planning on taking mostly Alteration and Conjuration spells, which I feel would suit him better from a more flavourful, roleplay perspective, rather than just choosing the typical "powerful" spells like fireball, etc.