Mites? Low humidity?

I don't know, Orleanders are fairly tolerant of very cool temps. I have mine in a garage where the winter temps range from a minimum of 38 F to a winter max of about 60. and they look fine. How cold is it getting in there? I also let mine get really dry at the cooler winter temps.

You do know that every single bit of that plant is highly poisonous, with no known antidote? Even inhaling the smoke from burning it can harm you.

It's a bit late to answer, but either over- OR under-watering can cause brown tips to leaves. I would review your watering practices - if too little water, I would really soak it and then let it drain, and if too much water, then make sure it isn't sitting in a puddle, and let the time between watering space out. You should water only when the top inch or so is dry when you stick a finger tip into the soil, not on a weekly or daily, set schedule - how dry the soil will be depends so much on the circumstances - how big the pot is, how root-bound the oleander is, how dry the air is, etc., etc..

As well, is it getting a lot of direct sun, esp. afternoon sun? If it had been in indirect light, then maybe it's getting too much sun, and if it is getting lots of direct sun, esp. afternoon sun, even if it WAS getting morning sun, it may be too much light as well as well.

The third possibility is that you over fertilized it the last time you fed it. If that's the case, then put it in the sink - or bathtub/shower - and run a lot of water through the soil/pot to wash out excess fertilizer and salts. You might do best with the regimen suggested for orchids, fertilize weekly, weakly. Mix a soluble fertilizer at a quarter the recommended strength, and water with that mix every time you water. However, if it was over fertilized, I would wait a month or so before feeding the oleander anything at all!

Fourthly, you may need to repot it - the plant may be root-bound. If you want to keep it in the same pot, then you probably should root-prune it, otherwise, move it up to a pot about 2" wider and deeper than the pot it is now in.

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