My current TV is not a "smart TV" - Samsung Plasma.
I tried hooking up the DTV box to the intard webz once, I tired to download a movie and I tried to stream a movie, neither worked because my intardwebz connection is a DSL that's slow.

I can watch movies streamed from Netflix and Amazon using their standard definition download speeds using a wireless connection from my laptop.

I am looking at buying a new TV, they all seem to be some sort of smart TV.
My question is this - Does a smart TV need to be hooked up to the intardwebz all the time to work as a TV?
Or will I get all sorts of alerts, warnings and notices that the TV needs an intardwebz source.

I did the Google thing and I looked in this forum, I didn't find an answer I was looking for.

Thanks!

It will work fine with no internet.

Thanks!

TV does not have to be hooked up to internet but it will need to be for software/firmware updates and DSL will work fine.

My TV isn't a smart TV thus I use either my Xbox 1 or PS3. Mainly my Xbox 1 for streaming cause after I got it I really don't use my PS3 other than a few games.

I have no idea what those are and I have no desire to learn (not a gamer).
I wireless my laptop from the router and I HDMI the laptop into the TV.

Run a wire from your router to your TV.  Wireless is for portable things, and sucks for trying to watch TV.

Since your question has already been answered I would like to add that if you set-up a pi-hole it will block all those adds and commercials.  I set my router to use DCHP  and now my smart frig doesn't tell the gubermint how much meat I eat.  Lol.   Of course I only use the T.V. to watch Lions games.

This should get you going if you're interested:
Why you need a network-wide ad blocker
Setting up a pi-hole step-by-step

I am a PC gamer and got those for some games to play. If you have a laptop with HDMI output then you are good to go just got to get the apps and then change the display to the TV. The console like Xbox just is easy for most of it till you have to put in email and password. That is a bitch without a keyboard.

I did. DSL is too slow no matter if it's wired or wireless for the DTV streaming stuff.

Using Amazon or Netflix wired won't get me HD TV, the DSL is too slow.

Using SD I can wireless it or I can use a wire, it doesn't matter. Wireless is easier.