Do I really need a separate night cream, or is my day moisturizer enough?

Not a requirement — what matters is the texture and whether it's doing a job your daytime moisturiser isn't, like carrying a heavier occlusive or an overnight active.

"Night cream" is largely a marketing category, not a functional necessity. What actually differs between a good day and night routine is that daytime needs to layer under sunscreen (so lighter, non-greasy) while nighttime has more room for a richer, more occlusive formula or one built around an active like retinol that shouldn't be worn in the sun. If your daytime moisturiser is comfortable to sleep in and doesn't need to make room for an overnight active, a second product isn't required.