I received taxi instructions from ground at a class D airport in the USA as follows (I was at ramp): Taxi to runway 04, Right on Bravo, left on 10, right on Alpha (no explicit clearance or hold short instructions for 10 were given). 10 was an inactive runway that intersected 04 with the Alpha taxiway turning off prior to the intersection with 04. I held short when I got to the 10 threshold and asked for clearance to taxi on the runway. The controller followed with Taxi left on 10, right on Alpha, but again no explicit clearance to enter the inactive runway at which point I taxied as instructed. My question is did I need to ask for clearance to taxi on the runway given the original instructions above?
Yes, you need an explicit instruction (not clearance) to taxi on any runway - and you got one!
The controller told you to "taxi on [runway] 10" which is about as explicit as it gets. If he did not want you to taxi onto the runway, he would have explicitly told you to hold short of runway 10. Note that it doesn't really matter if the runway is "active" or not. In the eyes of ATC, a runway is always a runway. Don't expect the controller to say something like "cleared to enter runway xx" - because it is not a clearance, but an instruction. The phraseology used will be along the lines of "enter runway xx", "taxi on runway xx", "cross runway xx" etc. - never "cleared". The only time you will hear "cleared" and "runway" in the same sentence is in a takeoff clearance or landing clearance.
That said, you did exactly the right thing. If in doubt, stop and ask. Especially when it comes to runways, if in doubt, never assume you have been instructed to enter a runway. Runway incursions are very dangerous, and the controller would much rather clarify an instruction instead of risking a collision.
J. Hougaard is correct. In “FAA-land” you also need clearance from ATC to be on a runway regardless of if you are in an airplane or not. You do not have to hear the words “clear” or “cleared”.
Typically, the instruction you get will be to “cross”, “taxi”, “back-taxi”, or “Line Up And Wait”. I’ve even heard the probably non-standard “do a 180”. If ATC does not want you to enter the runway, they typically say “Hold”, “Hold at” or “Hold short”. In my experience, that will be the last instruction in their string of instructions.
They typically will delay giving you further instructions until they are ready to clear you to enter the runway. I believe that is not always the case. ATC may be allowed to give you instructions in their entirety the first time to allow you the opportunity to write them down prior to beginning your taxi. It is still your responsibility to stop your aircraft wherever they told you to Hold until cleared to proceed.
As a paratrooper jumping onto an active airfield, we had spotters in touch with ATC stopping us at the edge of the runway until they received clearance for us to cross on foot. Nothing like staring down a Southwest Airlines 737 on takeoff coming straight at you at over 100 knots (actually happened). Those engines are much lower to the ground than a C130. I was not thinking of runway incursion reports when the wing passed over our heads.