You automatically get a road when you found a city, so there will always be at least one trade arrow in each city.
For a river terrain, yes.... for Mountains, forests, galciers, tundra you won't, unless some specials. I like building on hills for protection and irrigation + mining (settlers must work in groups of 2 or 3 for mining), and this is where I really would like that arrow

.
Roads also reduce corruption when connected to the capital via the "correct" route, plus increase trade bonus by 50% and trade by 50% (if the right route is roaded.... just any old road will not do).
I like roading over a hill, or even mountain, in early game, so I can set and win a barb trap. 150g in early game comes in handy! And fighting outside your city eliminates pop loss if you lose.
You can successfully irrigate a wheat in Despotism, BTW (e.g., you get extra food). That's because of the way production is reduced & rounded (see Nethog's Civ 2 Info Pack, which can be found in the Info link in my sig block for summaries).
I road first, and irrigate my capital and/or SSC as early priority.