Arashiyama Itinerary in 3 hours

Hi, I am planning to add Arashiyama to our 1 and a half day itinerary in Kyoto. As we are on a very tight schedule, I was wondering which attractions should I fit into our 3 hour (max 3 and a half hour) itinerary there. I was planning on just going to Togetsukyo Bridge, the Bamboo Grove, and Tenryu-ju, but if more attractions can fit in to the our timeframe the better. Would these places still be good sights even though it's still winter time?

3 hours is doable if you dedicate an hour to each. I don't think there's much to do at Togetsukyo so maybe not a full hour is needed. I would use that extra time to check out some of the shops on the street leading to the bridge. As for Bamboo Grove, it took me about 45 minutes to walk through the whole thing and that's with me stopping for photos quite a number of times. Unfortunately I didn't spend that much time in Tenryuji so I can't advise you on that.

Is walking through the bamboo grove an option? I was just thinking of taking a few shots of the bamboo grove before moving to the next attraction. Also, I was also thinking of going to Iwatayama Monkey park, and we managed to stretch our schedule for about 30 minutes to an hour so I was wondering if the view of Kyoto up there is worth the time.

Yes, you actually walk through the bamboo groves.

Note that if you walk all the way to the end on the west side, it's a fairly long walk along the river to the Togetsukyo Bridge.