IF there is something dangerous, according to Murphy's Law, your horse will find it, get hurt and You will have a new Vet bill.
I've been through wooden fencing and electric fencing (where I rented a paddock/shelter) and when I moved to my current property, I used an old well built but falling apart cattle fencing with two stands of barbed wire on top.
If you have old, sedentary horses they might do ok for awhile with this. If not, I would look into replacing as much as possible in phases. First, remove the barbed wire and replace it with something like this: Field Guardian 1.5 Inch Polytape - Horse.com
This is very affordable and with a plug in, even though this one says it's only rated for dogs, it still will charge for a temporary fix: Red Snap'r 10 Acre AC Low Impedance Fence Charger - Horse.com
Go shopping online for another more powerful.
Then, you need to assess what you currently have. How many wooden posts do you have and how many do you need?
You can create a budget and make this work.
CAUTION: When you take out the barbed wire be VERY CAREFUL! You can get cut easily, and it can spring into your face, so:
1) buy/wear long "welder's gloves"
2) buy/wear plastic safety glasses
3) buy/use a new pair of wire cutters. I recommend a fencing tool: Fence Pliers - Horse.com
(I have a pair and I used them to do fence repair before the property was refenced professionally.)
4) wear leather boots
When you cut barbed wire sections, carefully fold them up several times. Keep your plastic grain bags bc they are excellent for stuffing with old wire, like this and disposing and they don't break easily.
Finally, a very good solution is to keep the electric on top and buy a 100 ft. roll of cattle or horse fencing to stretch out on the outside of your fencing.
I just grabbed THIS link, so you might want to shop around: Red Brand 11 Gauge Wire Field Fence (Height: 39") at Blain's Farm & Fleet
My 5 acres, which are divided into 7 different sections, cost about $21,000 in 2008.
What I have posted above will run YOU about $600.00 and maybe less.
Hope this helps. Been there...