Do you have to turn cellular data on to receive photo attachments by text?

Yes. MMS requires data.

I'm not familiar with the HTC phones - sorry. But for iPhone, you have always been required to have cellular data to receive MMS.

With iMessage though, you can receive it without cellular as long as you have wifi connection, and of course the sender needs to have iMessage as well. So, Apple products to each other only.

Can't directly address the HTC either, but MMS is a cellular service (just a media externsion of SMS, actually). If your HTC phone was sending MMS with cellular turned off, it most certanly had to have a function similer to iMessages that used WiFi.

On iOS, you can send images via iMessages, but only to onother iOS or OS X device.

That is a decision you need to make based on your usage habits and what your data allotment is. We couldn't advise you what you should do as everyone's individual needs are different.

I never turn off cellular on the phone - the phone function is still the primary use for me and there are some data sevices I prefer to keep on at al times. You can restrict some functions from using cellular however: Settings App > General > Cellular > and set as needed in the Use Cellular Data for section. Aslo Check location services and turn off those apps you really don't need location services for.

But ultimately I agree with pdrith. Monotor your cellular data (your provider may even have an app to do that - Verizon in the US does), and based on your plan make a decision about how much you need to worry about it.