Mushy, juicy leaves are a sign of over-watering, but soft limp leaves are a sign of too little water. Cold weather can also cause succulent leaves to be come softer or mushy, but I don’t think that’s the case here.
Since this is a new plant growing from a leaf it’s likely to show some changes that look like over or under watering. However, the mother leaf will start to shrivel at some point, so don’t base the health of the baby on that leaf.
Instead, make sure the baby is firm but not turning translucent. It looks really healthy to me right now so I’d keep doing what you’re doing.
If you’re still concerned about your succulent being exposed to the cold, you could invest in a grow light. It would provide some warmth as well as additional light that your succulent will need with the shorter, winter days. Heat mats are also low-cost and effective at keeping plants warm.
Luckily, your plant looks like it’s still pretty healthy. If you notice any significant changes, this post will walk you through helping it recover. Good luck!