I'm exclusively breastfeeding my baby, and occasionally give him pumped bottles. I generally try to warm them up before giving them to him, at least to room temperature. (I was once told as a tip to get babies used to room-temperature bottles right away, just in case sometime you don't have a way to heat it up...) Sometimes, though, he is frantically crying as I'm trying to warm up the bottle... Is it ok to give him a cold bottle? He doesn't seem to mind, and drinks the whole thing. Are there any problems with feeding a 2-3 month old a cold bottle?
The biggest risk is that the baby won't drink it. If your baby is content to drink cold milk, then it is perfectly fine.
I couldn't find any online resources from medical professionals discussing it, but I did find that you are not alone in your situation :) Lots of other mothers have had this same dilemma, and many in that discussion shared that they have not run into any problems (aside from some babies simply not liking their milk cold).
Edit: I found this link which references a chart that indicates how long breast milk can be stored at room temperature. Depending upon your pumping schedule, you may be able to simply keep a bottle out for that "I need food NOW" moment.
I did find research on the effect of milk temperature￼ on preterm infants at http://milkbank.com/pdf/Stanford_Study_milk_feeding_temperature.pdf
A summary of the results included the following statement: The infants in this study had a similar tolerance (as measured by gastric residuals) to both cool temperature milk (10°C) and room temperature milk (24°C). Based on these data, there appears to be no advantage to warming frozen or refrigerated milk to room temperature.
The study did reveal better tolerance for warmed milk for these fragile infants.
Yes, you can feed your baby a room-temperature bottle.
The reason is that infants are very small bodies, so temperature differences are more significant to them than to older kids or adults.
Infants can't handle a steaming hot cup of tea, just like they can't handle milk that's just a few degrees above freezing. The closer to the natural body-temperature their food is, the easier they can handle it.
By the way, the same idea applies to bath water. (For bathing, not drinking!)