You're welcome.
Reverse iterators make things a little easier. 
I think you could use the forward iterator but then you must start at v.end()1.
v.end() is invalid, so your for loop line 28 may not work.
You would also want to include v.begin(), which your for loop would stop at.
I think the only way you will get a carry > 8 (9*9 = 81 is max 1digit case) is if mult >=10 (ie greater than the base you are representing in).
In this case, I think the result will still be OK except for the last carry.
I tried modifying multiply to allow for a multidigit final carry, changing:
1 2 3 4

if( carry > 0 )// push_front the carry
{
v.insert( v.begin(), carry );
}

to:
1 2 3 4 5

while( carry > 0 )// push_front the carry
{
v.insert( v.begin(), carry%10 );
carry /= 10;
}

I tested this against finding 2^1000 = (32)^200 with:
1 2 3 4 5

vector<int> numbers;
numbers.push_back(1);
for( int i=1; i<= 200; ++i)
multiply(numbers, 32);

I still get the correct answer.
EDIT: max carry=9, not 8 for 1digit case. I forgot that carry would be summed so max case is 9*9 + 9 = 90
Testing theory re. use of forward iterator in multiply:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

void multiply2(vector<int>& v, const int mult)
{
vector<int>::iterator it = v.end()1;
int product= (*it)*mult;// 1st term explicitly
int carry = product/10;
*it = product%10;
while( it != v.begin() )
{
it;// so v.begin will be included
product = (*it)*mult + carry;
carry = product/10;
*it = product%10;
}
while( carry > 0 )// push_front the carry
{
v.insert( v.begin(), carry%10 );
carry /= 10;
}
}

This works too.
@ne555 and cire. I would store the digits in the opposite order too and use push_back for the carries, but bickels had it setup as low digit last. I was just trying to make it work that way.