Baby is 7months and for the last several weeks she has only wanted to sleep on her side. I put her down on her back but she will always roll to either side. I have tried rolling her back onto her back but she wakes. Is there a safe way to keep her on her back? Or is it okay for her age to be on her side? Also are mittens a bad idea? Her hands are so cold with this weather. But I’m hoping it doesn’t interfere with her rolling back if she manages to roll onto her tummy.

What you are describing is normal development.
Most babies will be rolling over by 4 - 6 months…. some earlier
This is very normal as babies grow & become stronger many babies then prefer to sleep on their tummy, & often don’t change from that position.
This is not something that needs to be stopped, but it is important to make the environment as safe as possible for this to occur.

Always place baby on their back to sleep.
Transfer to cot if not already.
Ensure cot mattress is firm, well-fitting & flat.
Ensure there is nothing loose or soft in the cot.
Use a sleeping bag now that has appropriate size neck & arm holes if appropriate….. cease wrapping if you have not already done so.
It is essential to discontinue wrapping as soon as baby starts showing signs that they can begin to roll..
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over

Red Nose has the following information now that your baby is starting to roll.

Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lamb’s wool, doonas, pillows, cot bumpers or soft toys)
As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort
By this stage it is not necessary to wake during the night to turn baby over to the back position

Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.org.au/article/is-it-safe-to-use-products-designed-to-keep-baby-in-a-particular-position

Mittens are not necessary, as baby’s hands will often feel cold, however, it is important to ensure they are not thick (padded) & baby cannot suck on the material if you plan on using them.
Many babies like to touch their face.