Paso de Cortés to La Joya
My brother Noah organised this out-and-back hike since we’re in Cholula. It’s about a 1.5–2 hour drive from town, starting from the main ranger station.
Paso de Cortés is the mountain pass crossed by Hernán Cortés, Spanish forces, and indigenous allies on the way to Tenochtitlán (modern Mexico City) in 1519. If you haven’t already, read up about or watch a primer on the Conquistadores. Hectic.
Walking to La Joya and then back to the ranger station took us just over three hours at a leisurely pace, including breaks. It was fairly easy, though we timed it well with weather and had been at Puebla-level altitude for over a week before.
We didn’t wear or take anything special (not even poles) and were totally fine. Continuing from La Joya towards Iztaccíhuatl looked like a step up, though. Most people had helmets, poles, and sometimes also snow gear.

I believe you need to register with the national park service at least five days out of either driving a car up to La Joya, camping, or attempting Iztaccíhuatl. For the hike to La Joya we were able to just just turn up on the day and pay the standard MXN$175 park entry fee per person.
Your milage may vary. With all of the above.