Druids get twelve spells at 4th level, nine of which have carried over at the same level from OD&D. Two spells are new (call woodland beings and repel insects), while hold plant used to be a 5th-level spell. OD&D druids could cast insect plague as a 4th-level spell, but in AD&D that's been bumped up to 5th.
Animal Summoning I: Allows the druid to summon up to eight animals of a type of his choosing, as long as the animals have no more than 4HD each and are already found within the spell's range. This is potentially very powerful, but it's also completely subject to the DM's whim, as it's the DM who gets to determine how likely it is that the named animal is present.
The OD&D version of the spell was almost completely different, in that it allowed the summoning of one large animal, 3 of medium-size, or six small animals. Obviously it was lacking in power, but it also didn't have the stipulation of the animals already being present.
Call Woodland Beings: Works much like animal summoning, but instead of animals it calls a set number of woodlands creatures, e.g. 2-8 brownies, 1-4 centaurs, 1 treant, etc. Again, it's up the the DM to determine if the desired creature is present. If there are evil characters accompanying the druid, the summoned creatures will flee if they make a saving throw, and regardless of alignment they need to pass a loyalty check if the druid asks them to fight.
Control Temperature 10' Radius: Allows the druid to alter the temperature up or down by 9 degrees Fahrenheit per caster level - which could get potentially deadly for anyone within range, even though no concrete spell effects are given. If there's one limiting factor it's that the spell is centered on the druid, and there's no indication that the caster is immune to the spell's effects. It's probably intended more as a way to offset environmental hazards, but if you get a high-level druid who somehow gains immunity to heat or cold, and the ability to raise temperatures by 100 degrees+, that could get very dangerous. The OD&D version of the spell had a maximum temperature variation of 50 degrees up or down, which was probably for the best.
Cure Serious Wounds: Just like the cleric spell of the same name, except that it requires mistletoe to cast.
Dispel Magic: Just like the cleric spell, but it has a longer range and larger area of effect, and it also requires mistletoe.
Hallucinatory Forest: Creates an illusory forest that affects those within it as though it were real. Other druids will recognise the illusion, as will certain forest-dwelling creatures (such as centaurs, dryads, nymphs, satyrs, treants and even green dragons), and the spell can be negated with dispel magic or a reversed hallucinatory forest. There's no indication of whether characters within can attempt to disbelieve, as they can with many other illusions. The only mechanical difference from OD&D is that the original spell had a fixed shape (3" square per level); in AD&D the spell has a larger area and can be shaped into a square or rectangle as the caster wills.
Hold Plant: Can be used to stop/paralyze any form of plant life, including various plant monsters and funguses. It even specifies that it stops plants from making noise, which means that it can stop a Shrieker from doing its thing. Like hold person it can target multiple plants, but it's more effective the less targets there are. As for the OD&D spell, it seems that that version couldn't affect regular plants: as it said, "this spell will affect only vegetable matter which is self-ambulatory or magically animated".
Plant Door: If I'm reading this correctly, the spell allows the caster, higher-level druids and dryads to pass freely through trees and undergrowth, and also allows the caster to step inside a tree trunk and hide for the duration of the spell. For some reason, druids can't hide for as long inside an ash tree, which might make sense to tree-heads but means zilch to me. The major difference from OD&D is that the path created is now taller and wider, and it's length is based on caster level.
Produce Fire: Creates a 12' square area of fire that burns for a single round, deals 1-4 damage to everyone within, and sets combustibles alight. It can also be reversed to put fires out, but to my eyes it seems a little weak for its level. The OD&D spell had a smaller area and a lower range, and didn't specify damage dealt.
Protection From Lightning: Just like protection from fire, but for lightning - meaning that it grants immunity to normal lightning and a hit point buffer against magical lightning. The OD&D spell was different, in that it granted complete immunity to all lightning, but was negated after the first bolt.
Repel Insects: Creates a barrier that wards out all normal insects. Giant types with 2 or more HD can pass through if they make a saving throw, but will still sustain 1d6 damage. It only works on actual for real insects, not spiders and scorpions and such - so it requires some genuine real-world knowledge.
Speak With Plants: Just like the cleric spell, but has a longer duration and a greater area of effect. It also requires mistletoe.