Mountain Dwarves make strong Wizards, especially if they do not bother with heavy armor or shield and just use medium armor. Or alternatively wait until their Int is 20 and then go for heavy armor (but that is real high level, 19).
Let's do a little math.
Wizards start out with an average of 100 GP. This means that a player could easily afford 50 GP Scale Mail (if he is not worried about Stealth at all). Dex 14 and his AC is 16. Compared to the Dex 16 Human who pushed his Dex to 16 in order to get AC 13.
The human wizard used 18 of his ability score points out of 27. He now has 4 stats of 9 of which he'll probably make 3 of them a minimum of 10 (with one dump stat). Now he's down to 6 points left. So he makes CON 14 for the precious 2 hit points and has 1 point left over to probably bump his dump stat to 10. So Int 16, Dex 16, Con 14, one 11 and the rest 10 (or whatever).
This human has 8 hit points and AC 13. A human wizard could have 9 hit points, but then all of the rest of the stats are 9s. Meh.
The dwarf gets 15 Int 14 Dex 16 Con and 6 points to spread around the other stats (possibly 10 Str, 12 Wis, 10 Cha, or whatever).
The dwarf has 9 hit points and AC 16. His remaining 3 stats are equal or better than the human's.
The dwarf also has Darkvision (plus a few minor racial abilities). The human will need to cast a spell for that at higher level. The human does not suffer disadvantage for stealth.
The human has one more spell to choose from per day, but that might be Mage Armor and the dwarf will almost never take it. The human is at +1 to hit and -1 to foes saving against his spells.
But with many foes that start out with +4 to hit, the human had better use his extra spell to cast Mage Armor every day to get up to AC 16 as well. If he doesn't, then even Goblins can hit him on a 9 (60% of the time) for 5.5 average points of damage and 8 maximum. AC 16 drops that to 45% of the time.
Granted, a critical will take out either Wizard.
But the average number of rounds for a single Goblin to take out each Wizard is:
No Mage Armor human: 2.44 (3.10 if he gets one Shield spell off)
Mage Armor human: 3.21 (3.73 if he gets one Shield spell off)
Dwarf: 3.61 (4.14 if he gets one Shield spell off)
At first level against a Goblin, the no Mage Armor human will last 67% of the time of the Dwarf (75% with one Shield spell). Unless he attacks the goblin first or criticals or casts Shield, his odds of survival are somewhat slimmer (and casting both Mage Armor and Shield eats up a lot of his spells, there is only the recovery one left shy of cantrips). That extra round plus that the dwarf is standing allows him to get one more cantrip cast.
In order to stay even close to the dwarf with survivability, the human has to use up his extra spell per day on Mage Armor.
At level 4, the human and dwarf have the same number of spells and the same bonuses to hit and with saves vs. their spells, but the human still may have to cast Mage Armor once in a while. The dwarf also has 4 more hit points. The dwarf might also either remove the disadvantage for Stealth by acquiring a breastplate, or he might just stick with that and get his AC 1 higher if he can manage half plate.
They seemed balanced to me. The dwarf does a little less damage, but survives a lot better at levels 1 to 3 (which are very short time frame levels). The human either casts mage armor each day, or he's in a world of hurt if something nasty gets in his face.
Granted, most of us do not know how bracers or other magic items will work out. The human might be able to create a bunch of Mage Armor scrolls and acquire an additional 1st level spell and another spell option back each day, etc.
But there is one thing that the OP is correct about. If you wizard gets knocked down to zero hit points, it does not matter how many spells he has remaining or what his intelligence might be.
