I have been looking at putting a set of 12X7 rims with possibly 27X10-12 on front and 27X12-12 on the back. Do I need to be concerned about offset. Will I need a lift kit?
Thanks in advance.

 

I wouldn't I had a 2001 450ES and it would struggle with over sized tires like that even on packed flat trails let alone Mud or inclines.
You will need atleast the gear reducers http://www.ebay.com/itm/NEW-HONDA-FO...-/390319735576 with tires that big with the 24hp OHV 433cc turning them.

A 680 Rincon would struggle with those size tires.

Big mud tires in a mud hole or going up a steep incline do no good if they can't turn.

 

would the 26" tires be ok without the gear reducers?

 

It goes by tire weigh. My 26x11 with 1.19" lugs Zillas are as light as smaller 25x10 with a shorter 1" lug Mudlite XLs.
Even though Zillas are taller and wider.

Here is a good site that give you tire specs of all brands. Keep a eye on tire weights and lug depth.
ATV Mud Tires : Best ATV Tires

Maxxis Zillas are the lightest 6ply mud tire made with a aggressive lug. http://www.mud-throwers.com/inc/sdetail/6590/12045 That's why I chose them for a 350 4x4.

27x10 on the front is a large heavy tire. You can reduce weigh by reducing the width and leaving the height alone.

 

That's a very interesting option. I wonder why more folks don't use a
kit like that. It is not an unreasonable cost at all.

I have had the 04 Foreman 450FE, and currently use my TRX300FW all the
time to get up my 40% trail on my property (with new AT489s). I would
not want to lose ANY torque at the wheels. If anything, a smaller tire
diameter would be attractive, even with the lower clearance.