I have a new mobile home 200amp service and I have built a pedestal and am installing both a meter box and a service disconnect which is about 42" from the trailer. Every website I have found recommends 2/0THHN copperwire for the two hot leads and 1/0 copper wire for the neutral. Is this correct or do I need different sized wire?

That's fine for 200 Amps.

Since the service point will outside of the trailer, you cannot use THHN type conductors.

THHN is listed for use in "Dry" locations only.

THHW is listed for Wet areas, also THWN-2, XHHW and XHHW-2. All of these would have to be in conduit.

Using a multi conductor cable listed for direct burial (Type USE) is also a better choice.

One more thought, because you are putting in a main disconnect switch at the meter, you cannot use Table 310.15(B)(7) to select your service entrance conductors 200 amp - 2/0 cable.

You must use a 4 wire connection from the disconnect switch to your service panelboard. Which means that you need to use Table 310.15(B)(16). A 200 Amp feed requires a 3/0 cable if both the switch and the panelboard are listed for 75 (C) {167(F)}. If they are not listed for that temp, then you have to use the 60 (C) column which means that you would need a 250 kcmil cable.

I am guessing/assuming the wire was THHN/THWN, as that is what most Electrical Supply House carry.
Insulation is Important.

Since the service point will outside of the trailer, you cannot use THHN type conductors.

THHN is listed for use in "Dry" locations only.

THHW is listed for Wet areas, also THWN-2, XHHW and XHHW-2. All of these would have to be in conduit.I realize this is a very popular thing to correct on message boards, but these days it is a non-issue. Most people just say THHN as a matter of habit, and pretty much all THHN is also dual rated THWN these days.

One more thought, because you are putting in a main disconnect switch at the meter, you cannot use Table 310.15(B)(7) to select your service entrance conductors 200 amp - 2/0 cable.

You must use a 4 wire connection from the disconnect switch to your service panelboard. Which means that you need to use Table 310.15(B)(16). A 200 Amp feed requires a 3/0 cable if both the switch and the panelboard are listed for 75 (C) {167(F)}. If they are not listed for that temp, then you have to use the 60 (C) column which means that you would need a 250 kcmil cable.Don, just because there is a switch outside does not mean these are not still the main power feeder conductors. NEC 2011 Table 310.15(B)(7) still applies.

Remember, this table is for "Single-Phase Dwelling Services and Feeders"