But won't that mess with its type?
http://www.psypokes.com/dex/hp.php
That gives a chart of the highest possible IVs for a given HP-type and it also gives an HP-type calculator for any given set of IVs.
http://www.gamefaqs.com/boards/989552-pokemon-black-version/58772271
That thread gives a list of all IV combos for a given HP-type of power 70. The two tools are a bit outdated since in gen 6, HP is always 60BP. (In gen 5, it varied, up to the max of 70BP.) The calculating of the type is the same though.
FYI, the type of HP is calculated as follows:
(1) The only thing that matters is the IVs and their "least significant bits", or "LSB". The LSB is 0 if the IV is even and the LSB is 1 if the IV is odd.
(2) Arrange the 0's and 1's in the following order: (SpD)(SpA)(Spe)(Def)(Atk)(HP). So you get a string of 6 bits, which represents any number from 0 to 63, in base 2.
(3) The number (in base 10) then determines the type by the following chart:
0-4: Fighting
5-8: Flying
9-12: Poison
13-16: Ground
17-20: Rock
21-25: Bug
26-29: Ghost
30-33: Steel
34-37: Fire
38-41: Water
42-46: Grass
47-50: Electric
51-54: Psychic
55-58: Ice
59-62: Dragon
63: Dark
(Note that HP cannot be Normal- or Fairy-type. Also note that some types are more likely than others, particular Fighting-, Bug-, and Grass-types.)
Okay... now to answer your question: What is the least possible value of Atk IV to get a HP-type of Ice? The IVs must give a 6-bit string that represents a number from 55-58. That means the two leftmost bits must be 1 (so SpD and SpD must be odd). That leaves anywhere from 7 to 10 to make up. The Atk IV determines the power of 2^1 in the number. Each of the numbers 7 through 10 has the following binary expression (last four bits of the 6-bit number):
7---> 0111
8---> 1000
9---> 1001
10--> 1010
So clearly we are going to have to make a compromise on one of the IVs. We cannot have Atk=0 and all the others 31 (since that would be the string 1101, which does not appear). So it depends on which IV you want to lose points in. So the verdict is as follows:
HP-Ice is possible with the following IV spread, allowing Atk to be as low as possible (0 or 1) and all others as high as possible (30 or 31): all spreads must have SpD=SpA=31. There are then 4 possibilities for the others:
(1) Spe=30 Def=31 Atk=1 HP=31
(2) Spe=31 Def=30 Atk=0 HP=30
(3) Spe=31 Def=30 Atk=0 HP=31
(4) Spe=31 Def=30 Atk=1 HP=30
Choose your pleasure. (Remember that these are the only viable choices since all that really matters ultimately is whether the IV is even or odd. An IV of 29 is the same as an IV of 31 in the same stat.) I would probably just go with option (3). Options (2) and (4) lower two IVs. So it's either option (1) (lower Speed) or option (3) (lower Defense).