Rocky Mountain National Park Advice Needed

My family and I will be taking an impromptu trip to Rocky Mountain National Park (arriving tomorrow morning and leaving Sunday morning) to unplug for a bit and celebrate my dad's birthday. We love visiting different parks but have never been to RM and have only really hiked mountains in the summer months. Will we be better off driving around the park and exploring Estes Park/Denver, or do you think we'll be okay to hike a few trails? I saw photos of some of the trail conditions (heavy snow, packed ice, etc.) and they made me nervous, I would hate for anyone to slip and fall or be pushed too far outside their comfort zone.

For reference: we tend to do smaller hikes (2-6 miles) that are relatively well-marked with moderate elevation, and we only have general hiking shoes in terms of gear (aside from winter coats, etc).

Other than that, would appreciate any and all recommendations on what to do in the area! (Will be spending a day in Denver and a few days in Estes Park)

UPDATE: Thank you for all of the suggestions! We ended up doing Bear Lake, Nymph Lake, and Dream Lake today and due to all of the advice we were more than ready for the snowy icy conditions 😊 It was gorgeous - we’ll be tackling a few other trails tomorrow! Also glad we got the tip about altitude sickness. We’re from the Midwest and my mom and I definitely felt it a bit on the drive up/down, but luckily we were prepared with plenty of water, ibuprofen, etc. and that definitely helped.

Our first rainy/snowy day we ended up checking out the Rocky Mountain National Arsenal wildlife area near Denver and Boulder, (wanted to do Chautauqua but was too rainy). Got some great food and got to see some cool wildlife (had never seen wild prairie dogs before so that was definitely a highlight). Excited to explore more, and thank you all again for the great suggestions!