I've been putting my 11 week old baby in a fleece sleepsack for naps and bedtime, just to make sure she's cozy and not going to get chilled if she squirms around. I just put it on over her clothes. We're in Seattle and it's been cool most days, and if it's sunny and the house warms, she's in a short sleeved onesie and pants, or a bubble suit type outfit, but in warmer clothes for naps regardless since we have a fan on and her room doesn't get direct sunlight.
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When out, I wear her a lot and we've done hats some if we go to the park and it is breezy. Otherwise, she's in her clothes since she's against our body heat. When in her car seat to go outside to the car or go in a restaurant and it's been chilly (ie 60s and cloudy), put a sweater on her and then put a light blanket around her lower body in the car seat. If it's sunny and warmer, then I don't add any layers. She is actually often kinda hot when I remove her from the car seat after traveling on a nice day, guess it gets warm in the backseat.
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Usually always wear socks. I haven't been worried about her being too cold for her health, but have started lately to be more mindful of her being warm enough just for her comfort, so I've layered her up a little more lately unless I myself am am very comfortable in shorts and a tshirt and flip flops around the house (then I don't layer her up as much).
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She was swaddled all day long the first 3 weeks or so - she was just more content that way. That was April, so it was still cool here most days.
HTH.