Are there any additively homomorphic encryption schemes over $\Bbb Z_2$ besides Goldwasser-Micali? I am aware of Goldwasser-Micali cryptosystem, which is additively homomorphic over $\Bbb Z_2$. 
Are there other schemes that satisfy this property?

Note: If one is willing to involve advanced tools like lattices one could get something stronger like FHE. I am looking for a simple cryptosystem not involving lattices or similar tools.
Any additively homomorphic encryption scheme (with a large enough message space), e.g. Paillier. To do so, let the message space of the homomorphic encryption scheme be $\mathcal{M}$, you encode your message space $Z_2$ as follows:


choose an even number from $\mathcal{M}$ to represent 0, and an odd number to represent 1. One obvious choice would be simply 0 and 1. Let's call the two $m_0$ $m_1$ respectively


To encrypt, you encrypt $m_0$ or $m_1$ (all other messages are not allowed) using the homomorphic encryption scheme as usual.

To do homomorphic operations, you do the homomorphic operations as usual. 

To decrypt, you decrypt as usual, then take mod 2 on the result to get your final result.

Here the parity of the values encodes messages in $Z_2$: even corresponding to 0, and odd corresponding to 1. We know


odd+odd $\rightarrow$ even (1+1=0 mod 2)
odd+even $\rightarrow$ odd (1+0=1 mod 2)
even+even $\rightarrow$ even (0+0=0 mod 2)
even+odd $\rightarrow$ odd (0+1=1 mod 2)


Thus it is correct.

The message space needs to be large enough so you can do enough number of addition operations without overflow (0 and 1 is actually the best choice to maximize the number of operations you can do).