Is it good breathing through your nose all the time?

Yes, there are millions of tiny hairs in your nose that catch dust, bacteria and other harmful particles thus preventing them from getting into your lungs.
Your nose is also designed to control air temperature - cold air travels through some curved nose tunnels and gets heated up to body temperature, thus preventing your throat and lungs from getting cold.

And your mouth won't get so dried out when you breathe through your nose!

Mouth breathing is designed for the fail-safe when nose gets stuffed. And it is less attractive to see someone w. his/her mouth hanging open. Observe the world - how many are mouth breathers?(Unless kids w. tonsil, adenoid problems.) Do you breathe thru mouth by choice?

yeah, actually calling someone a "mouth breather" is like an insult (although it shouldn't be, it could just mean someone's having problems with their nose)

The offensive "mouth breather" term generally is used when describing someone who may be of low intelligence or limited capacity, the same type of people who are often found slack-jawed and breathing from your mouth. Often used to describe "snot-nosed" kids or Xbox Live users who constantly breathe or pant into their headset microphone.

yes its healthier and dry mouth increases bad breath

yes. the nostrils warm up the air and filter the dust.