All birds are different when it comes to bathing, and it seems historically (for my guys anyway) that conures love bathing. I've had 2 green cheek conures and they both have absolutely loved bathing. My current green cheek, Bowie, is almost a year old and he gives himself a bath pretty much every day in his water bowl as soon as I fill it. Short of taking his drinking water away there would be no way for me to stop him, and in my opinion there isn't a reason to stop him. He gets in the shower with me when he wants to, I give all my birds the option every day when I get in, but Bowie the green cheek and Lita the Quaker typically have already had a bath in their big stainless steel water bowl first thing in the morning. So by the time I get in the shower they've already washed and dried. I fill their stainless steel bowl that is attached to their T-stand at least three times a day because of their bathing. My cockatiel hates baths, she has no interest at all in bathing (of course it's the dusty bird that hates baths), so I put her in the shower with me once a week just to help with the dust, especially if she's molting, as a warm shower helps them with pin feathers (getting the keratin sheaths from around the new feathers). My Senegal parrot is still pretty young and he hasn't decided if he likes showers or baths yet or not. He's never bathed on his own in his bowl, but he does tend to jump in the shower with me every day (I think because he just wants to be in there with me). I'm happy if he gets in every day, he smells good, his feathers look great, and it helps with molting.
My best answer to your question is that if your conure wants to bath every day, then let him! If he doesn't want to bath every day, then don't force him, I'd say giving a bird a bath that hates baths is something that should be done once a week or every other week, just like a child that doesn't like to take a bath. They need to stay clean but weekly or bi-weekly is enough, unless they get into something of course. But bathing every day won't hurt your conure, except the possibility of dry skin. Daily bathing won't ruin his feathers, birds in the wild bath daily or are in the rain daily, their feathers aren't negatively effected by water, rather the opposite. As I said their skin may dry out, and using a good aloe vera spray made for birds weekly or bi-weekly can help that problem. I use a bath/molt-ease spray made by Ecotrition that is specifically made for birds and contains not only aloe vera and lanolin, but also purcehn oil, which is the same oil they secrete naturally from their preen gland and they rub on their feathers with their beaks when they preen themselves. When they are dry you give them a couple of good sprays with it, wetting their feathers. I use it weekly on the cockatiel and the green cheek, the green cheek because he baths daily and it keeps his skin moisturized, and the cockatiel because she has been going through a horribly rough molt for the last month. It seems to help them both, but I use it sparingly because it is quite oily.
The blow dryer I'm not sure about, I've never tried it (I think it would freak my guys out). I'd be worried #1 about burning/cooking my bird, and #2 horribly drying their skin out. That being said you certainly don't want your bird to be chilled every day after his bath. I encourage you to allow him to take a warm bath daily if he wants to, it's good for them and if he enjoys it that much then it is very good for him, but I'd either dry him well with a towel and possibly keep him wrapped in a towel until he dries, or ideally (some solution to your problem) I'd get a bird-safe space heater or better yet a cage heater made specifically for bird cages, and each day after his bath you should dry him as best you can with a small towel and then place him in his cage by the heater until he's dry, then let him back out, or whatever his schedule is of course... This is only my personal opinion. If your house is that cold I'd be online finding a cage heater immediately, regardless of whether or not he bathes, as he should never be cold, and a cage heater made specifically for bird cages is a much safer and consistent solution than a blow dryer or a space heater.
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