Clothes for May baby

Jen • 40 years old. PCOS. Daughter born 5/25/17 after beating infertility! 💜 Daughter #2 born 3/21/2019. 🎉
This is probably a stupid question, but as a FTM I'm so confused. 
I live in the Northeast, and the temps in May are usually around 60-65 during the day and 50ish at night. 
Are fleece sleep n' play (like below) going to be too warm at night?